Sample records for density functional quantum

This book examines densityfunctional theory based on the foundation of quantum chemistry. Unconventional in approach, it reviews basic concepts, then describes the physical meanings of state-of-the-art exchange-correlation functionals and their corrections.

A time-dependent generalized non-linear Schrödinger equation (GNLSE) of motion was earlier derived in our laboratory by combining densityfunctional theory and quantum fluid dynamics in threedimensional space. In continuation of the work reported previously, the GNLSE is applied to provide additional knowledge on ...

The Hohenberg-Kohn theorem of DensityFunctional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Kohn-Sham spin-densityfunctional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. Here an efficient method for the simulation of quantum dots using density-function theory is developed; it includes the particle-in-the-box representation of the Kohn-Sham orbitals, an efficient conjugate-gradient method to directly minimize the total energy, a Fourier convolution approach for the calculation of the Hartree potential, and a simplified multigrid technique to accelerate the convergence. We test the methodology in a two-dimensional model system and show that numerical studies of large quantum dots with several hundred electrons become computationally affordable. In the noninteracting limit, the classical dynamics of the system we study can be continuously varied from integrable to fully chaotic. The qualitative difference in the noninteracting classical dynamics has an effect on the quantum properties of the interacting system: integrable classical dynamics leads to higher-spin states and a broader distribution of spacing between Coulomb blockade peaks.

We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as densityfunctionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing densityfunctionals for use in quantum algorithms.

This paper discusses the relationship between the Wigner function, along with other related quasiprobability distribution functions, and the probability density distribution function constructed from the wave function of the Schroedinger equation in quantum phase space, as formulated by Torres-Vega and Frederick (TF). At the same time, a general approach in solving the wave function of the Schroedinger equation of TF quantum phase space theory is proposed. The relationship of the wave functions between the TF quantum phase space representation and the coordinate or momentum representation is thus revealed

Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of DensityFunctional Theory to highly accurately determine

The energy gap and dipole moment of chemically functionalized graphene quantum dots are investigated by densityfunctional theory. The energy gap can be tuned through edge passivation by different elements or groups. Edge passivation by oxygen considerably decreases the energy gap in hexagonal nanodots. Edge states in triangular quantum dots can also be manipulated by passivation with fluorine. The dipole moment depends on: (a) shape and edge termination of the quantum dot, (b) attached group, and (c) position to which the groups are attached. Depending on the position of attached groups, the total dipole can be increased, decreased, or eliminated.

The density matrix theory, the ancestor of densityfunctional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the densityfunctional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

Full Text Available The density matrix theory, the ancestor of densityfunctional theory, provides the immediate framework for Path Integral (PI development, allowing the canonical density be extended for the many-electronic systems through the densityfunctional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving many-electronic systems.

Friction is a desired property in quantum dynamics as it allows for localization, prevents backscattering, and is essential in the description of multistage transfer. Practical approaches for friction generally involve memory functionals or interactions with system baths. Here, we start by requiring that a friction term will always reduce the energy of the system; we show that this is automatically true once the Hamiltonian is augmented by a term of the form ∫a(q ;n0)[∂j(q,t)/∂t]ṡJ(q)dq, which includes the current operator times the derivative of its expectation value with respect to time, times a local coefficient; the local coefficient will be fitted to experiment, to more sophisticated theories of electron-electron interaction and interaction with nuclear vibrations and the nuclear background, or alternately, will be artificially constructed to prevent backscattering of energy. We relate this term to previous results and to optimal control studies, and generalize it to further operators, i.e., any operator of the form ∫a(q ;n0)[∂c(q,t)/∂t]ṡC(q)dq (or a discrete sum) will yield friction. Simulations of a small jellium cluster, both in the linear and highly nonlinear excitation regime, demonstrate that the friction always reduces energy. The energy damping is essentially double exponential; the long-time decay is almost an order of magnitude slower than the rapid short-time decay. The friction term stabilizes the propagation (split-operator propagator here), therefore increasing the time-step needed for convergence, i.e., reducing the overall computational cost. The local friction also allows the simulation of a metal cluster in a uniform jellium as the energy loss in the excitation due to the underlying corrugation is accounted for by the friction. We also relate the friction to models of coupling to damped harmonic oscillators, which can be used for a more sophisticated description of the coupling, and to memory functionals. Our results open the

The maximum von Neumann entropy principle subject to given constraints of mean values of some physical observables determines the density matrix. Similarly the stationary action principle in the case of time-dependent (dissipative) situations under similar constraints yields the density matrix. The free energy and measures of entanglement are expressed in terms of such a density matrix and thus define respective functionals of the mean values. In the light of several model calculations, it is...

Nuclear quantum effects such as zero point energy play a critical role in computational chemistry and often are included as energetic corrections following geometry optimizations. The nuclear-electronic orbital (NEO) multicomponent densityfunctional theory (DFT) method treats select nuclei, typically protons, quantum mechanically on the same level as the electrons. Electron-proton correlation is highly significant, and inadequate treatments lead to highly overlocalized nuclear densities. A recently developed electron-proton correlation functional, epc17, has been shown to provide accurate nuclear densities for molecular systems. Herein, the NEO-DFT/epc17 method is used to compute the proton affinities for a set of molecules and to examine the role of nuclear quantum effects on the equilibrium geometry of FHF - . The agreement of the computed results with experimental and benchmark values demonstrates the promise of this approach for including nuclear quantum effects in calculations of proton affinities, pK a 's, optimized geometries, and reaction paths.

Like a Green function to propagate a particle's wavefunction in time, a Blue function is introduced to propagate the particle's probability and current density. Accordingly, the complete Blue function has four components. They are constructed from path integrals involving a quantity like the action that we call the motion. The Blue function acts on the displaced probability density as the kernel of an integral operator. As a result, we find that the Wigner density occurs as an expression for physical propagation. We also show that, in quantum mechanics, the displaced current density is conserved bilocally (in two places at one time), as expressed by a generalized continuity equation. (paper)

We present a simple quantum correction scheme for ab initio Kohn-Sham spin densityfunctional theory (KS-SDFT). This scheme is based on a mapping from ab initio results to a Heisenberg model Hamiltonian. The effective exchange integral is estimated by using energies and spin correlation functionals calculated by ab initio KS-SDFT. The quantum-corrected spin-correlation functional is open to be designed to cover specific quantum spin fluctuations. In this article, we present a simple correction for dinuclear compounds having multiple bonds. The computational results are discussed in relation to multireference (MR) DFT, by which we treat the quantum many-body effects explicitly

Interaction between phenomenological description of a multi-component mixture on the basis of entropy functional with members, square in terms of component density gradients and temperature, on the one hand, and description in the framework of classical and quantum statistical mechanics, on the other hand, was investigated. Explicit expressions for the entropy functional in the classical and quantum theory were derived. Then a square approximation for the case of minor disturbances of uniform state was calculated. In the approximation the addends square in reference to the gradient were singlet out. It permits calculation of the relevant phenomenological coefficients from the leading principles [ru

Densityfunctional theory (DFT), as a first-principle approach has successfully been implemented to study nanoscale material. Here, DFT by numerical basis-set was used to study the quantum confinement effect as well as electronic properties of silicon quantum dots (Si-QDs) in ground state condition. Selection of quantum dot models were studied intensively before choosing the right structure for simulation. Next, the computational result were used to examine and deduce the electronic properties and its density of state (DOS) for 14 spherical Si-QDs ranging in size up to ∼ 2 nm in diameter. The energy gap was also deduced from the HOMO-LUMO results. The atomistic model of each silicon QDs was constructed by repeating its crystal unit cell of face-centered cubic (FCC) structure, and reconstructed until the spherical shape obtained. The core structure shows tetrahedral (T d ) symmetry structure. It was found that the model need to be passivated, and hence it was noticed that the confinement effect was more pronounced. The model was optimized using Quasi-Newton method for each size of Si-QDs to get relaxed structure before it was simulated. In this model the exchange-correlation potential (V xc ) of the electrons was treated by Local Density Approximation (LDA) functional and Perdew-Zunger (PZ) functional

We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent densityfunctional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.

In this article, we prove the one-to-one correspondence between vector potentials and particle and current densities in the context of master equations with arbitrary memory kernels, therefore extending time-dependent current-densityfunctional theory (TD-CDFT) to the domain of generalized many-body open quantum systems (OQS). We also analyse the issue of A-representability for the Kohn-Sham (KS) scheme proposed by D'Agosta and Di Ventra for Markovian OQS [Phys. Rev. Lett. 2007, 98, 226403] and discuss its domain of validity. We suggest ways to expand their scheme, but also propose a novel KS scheme where the auxiliary system is both closed and non-interacting. This scheme is tested numerically with a model system, and several considerations for the future development of functionals are indicated. Our results formalize the possibility of practising TD-CDFT in OQS, hence expanding the applicability of the theory to non-Hamiltonian evolutions.

The ability to calculate accurate electron densities of full proteins or of selected sites in proteins is a prerequisite for a fully quantum-mechanical calculation of protein-protein and protein-ligand interaction energies. Quantum-chemical subsystem methods capable of treating proteins and other

Time-dependent densityfunctional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a noninteracting open Kohn-Sham system yielding the correct nonequilibrium density evolution. A pseudoeigenvalue equation analogous to the Casida equations of the usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C(2 +) atom including natural linewidths, by treating the electromagnetic field vacuum as a photon bath. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on the Görling-Levy perturbation theory is calculated.

Time-dependent [current]-densityfunctional theory for open quantum systems (OQS) has emerged as a formalism that can incorporate dissipative effects in the dynamics of many-body quantum systems. Here, we review and clarify some formal aspects of these theories that have been recently questioned in the literature. In particular, we provide theoretical support for the following conclusions: (1) contrary to what we and others had stated before, within the master equation framework, there is in fact a one-to-one mapping between vector potentials and current densities for fixed initial state, particle-particle interaction, and memory kernel; (2) regardless of the first conclusion, all of our recently suggested Kohn-Sham (KS) schemes to reproduce the current and particle densities of the original OQS, and in particular, the use of a KS closed driven system, remains formally valid; (3) the Lindblad master equation maintains the positivity of the density matrix regardless of the time-dependence of the Hamiltonian or the dissipation operators; (4) within the stochastic Schrödinger equation picture, a one-to-one mapping from stochastic vector potential to stochastic current density for individual trajectories has not been proven so far, except in the case where the vector potential is the same for every member of the ensemble, in which case, it reduces to the Lindblad master equation picture; (5) master equations may violate certain desired properties of the density matrix, such as positivity, but they remain as one of the most useful constructs to study OQS when the environment is not easily incorporated explicitly in the calculation. The conclusions support our previous work as formally rigorous, offer new insights into it, and provide a common ground to discuss related theories.

We present a rigorous formulation of the time-dependent densityfunctional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally v-representable. Spanish Ministry of Economy and Competitiveness (Grant No. FIS2013-46159-C3-1-P), Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13), COST Actions CM1204 (XLIC) and MP1306 (EUSpec).

A comprehensive review of the attempts to rephrase molecular quantum mechanics in terms of the particle density operator and the current density or phase density operator is given. All pertinent investigations which have come to attention suffer from severe mathematical inconsistencies and are not adequate to the few-body problem of quantum chemistry. The origin of the failure of these attempts is investigated, and it is shown that a realization of a local quantum field theory of molecular matter in terms of observables would presuppose the solution of many highly nontrivial mathematical problems

Highlights: · We augment a double-layer model based on integral equations by calculating the interaction parameters with the electrode from quantumdensityfunctional theory · Explicit model calculations for Ag(1 1 1) in aqueous solutions give at least qualitatively good results for the particle profiles · Ours is the only method which allows the calculation of capacity-charge characteristics. · We obtain reasonable values for the Helmholtz (inner-layer) capacity. - Abstract: We have complemented the singlet reference interaction site model for the electric double layer by quantum chemical calculations for the interaction of ions and solvents with an electrode. Specific calculations have been performed for an aqueous solution of NaCl in contact with a Ag(1 1 1) electrode. The particle profiles near the electrode show the specific adsorption of Cl - ions, but not of Na + , and are at least in qualitative agreement with those obtained by molecular dynamics. Including the electronic response of the silver surface into the model results in reasonable capacity-charge characteristics.

We have studied the structural stability of monolayer and bilayer arsenene (As) in the buckled (b) and washboard (w) phases with diffusion quantum Monte Carlo (DMC) and densityfunctional theory (DFT) calculations. DMC yields cohesive energies of 2.826(2) eV/atom for monolayer b-As and 2.792(3) eV/atom for w-As. In the case of bilayer As, DMC and DFT predict that AA-stacking is the more stable form of b-As, while AB is the most stable form of w-As. The DMC layer-layer binding energies for b-As-AA and w-As-AB are 30(1) and 53(1) meV/atom, respectively. The interlayer separations were estimated with DMC at 3.521(1) Å for b-As-AA and 3.145(1) Å for w-As-AB. A comparison of DMC and DFT results shows that the van der Waals densityfunctional method yields energetic properties of arsenene close to DMC, while the DFT + D3 method closely reproduced the geometric properties from DMC. The electronic properties of monolayer and bilayer arsenene were explored with various DFT methods. The bandgap values vary significantly with the DFT method, but the results are generally qualitatively consistent. We expect the present work to be useful for future experiments attempting to prepare multilayer arsenene and for further development of DFT methods for weakly bonded systems.

We present densityfunctional theory (DFT) and quantum Monte Carlo (QMC) calculations of the glutamic acid and glutamate ion in vacuo and in various dielectric continuum media within the polarizable continuum model (PCM). In DFT, we employ the integral equation formalism variant of PCM while, in

Full Text Available This paper presents a systematic study of the absorption spectrum of various sizes of small hydrogenated silicon quantum dots of quasi-spherical symmetry using the time-dependent densityfunctional theory (TDDFT. In this study, real-time and real-space implementation of TDDFT involving full propagation of the time-dependent Kohn-Sham equations were used. The experimental results for SiH4 and Si5H12 showed good agreement with other earlier calculations and experimental data. Then these calculations were extended to study larger hydrogenated silicon quantum dots with diameter up to 1.6 nm. It was found that, for small quantum dots, the absorption spectrum is atomic-like while, for relatively larger (1.6 nm structure, it shows bulk-like behavior with continuous plateau with noticeable peak. This paper also studied the absorption coefficient of silicon quantum dots as a function of their size. Precisely, the dependence of dot size on the absorption threshold is elucidated. It was found that the silicon quantum dots exhibit direct transition of electron from HOMO to LUMO states; hence this theoretical contribution can be very valuable in discerning the microscopic processes for the future realization of optoelectronic devices.

In the semiconductor industry, the use of new materials has been increasing with the advent of nanotechnology. As critical dimensions decrease, and the number of materials increases, the interactions between heterogeneous materials themselves and processing increase in complexity. Traditionally, applications of ab initio techniques are confined to electronic structure and band gap calculations of bulk materials, which are then used in coarse-grained models such as mesoscopic and continuum models. Densityfunctional theory is the most widely used ab initio technique that was successfully extended to several applications. This paper illustrates applications of densityfunctional theory to semiconductor processes and proposes further opportunities for use of such techniques in process development

We use the exact strong-interaction limit of the Hohenberg-Kohn energy densityfunctional to construct an approximation for the exchange-correlation term of the Kohn-Sham approach. The resulting exchange-correlation potential is able to capture the features of the strongly correlated regime without

We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general formulation, that needs the fully correlated many-electron wavefunction, can be simplified by making use of time-dependent density-functional theory. In this case, the optimal control equations require some modifications that we will provide. The abstract general formulation is complemented with the simple example of the H 2 + molecule in the presence of a laser field. (paper)

A brief discussion and resume of density operator formalism in the way it occurs in modern physics (in quantum optics, quantum statistical physics, quantum theory of radiation) is presented. Particularly we emphasize the projection operator method, application of spectral theorems and superoperators formalism in operator Hilbert spaces (Hilbert-Schmidt type). The paper includes an appendix on direct sums and direct products of spaces and operators, and problems of reducibility for operator class by using the projection operators. (author)

The state of the art of the densityfunctional formalism (DFT) is reviewed. The theory is quantum statistical in nature; its simplest version is the well-known Thomas-Fermi theory. The DFT is a powerful formalism in which one can treat the effect of interactions in inhomogeneous systems. After some introductory material, the DFT is outlined from the two basic theorems, and various generalizations of the theorems appropriate to several physical situations are pointed out. Next, various approximations to the densityfunctionals are presented and some practical schemes, discussed; the approximations include an electron gas of almost constant density and an electron gas of slowly varying density. Then applications of DFT in various diverse areas of physics (atomic systems, plasmas, liquids, nuclear matter) are mentioned, and its strengths and weaknesses are pointed out. In conclusion, more recent developments of DFT are indicated

Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal densityfunctional are required. In this work, a model based on deep learning is developed to approximate this functional. Deep learning allows computational models that are capable of naturally discovering intricate structure in large and/or high-dimensional data sets, with multiple levels of abstraction. As no assumptions are ...

One-particle propagators of the relativistic electron--positron gas are systematically investigated. With the nonvanishing chemical potential the neutrality of the whole system is secured by a uniformly charged classical background described by a classical current J/sub μ/. Due to the translational invariance of this model it is natural to investigate the properties of the propagators in the momentum space. The Fourier-transforms of the Green's functions have been expressed in terms of the generalized spectral Lehmann representation and the second-order spectral functions of the photon and electron propagators have been found. The matter-dependent part of the propagator is finite and only the vacuum part has to be renormalized with the use of standard renormalization counterterms. The singularities of the gauge-independent photon propagator have been further investigated with the use of the spectral representation and nonperturbative expressions for the spectrum of collective excitations have been obtained. In the second order of perturbation they reproduce the asymptotic formulas at T→0 and T→infinity cited previously in the literature. In particular, the relativistic plasma frequency (photon effective mass) has been expressed in a simple form in terms of the integrals over the spectral functions. Our formulas for the relativistic plasmon mass squared Ω 2 exhibit an interesting property that at some temperature and density Ω 2 should become negative. However, simple estimates show that this phenomenon occurs at highly nonrealistic temperatures of the order of e 137 , i.e., in the region where the perturbation theory fails. The damping of the collective excitations is also considered

We present the first application of quantum Monte Carlo (QMC) in its variational flavor combined with the polarizable continuum model (PCM) to perform excited-state geometry optimization in solution. Our implementation of the PCM model is based on a reaction field that includes both volume and

The review generalizes the results of structural studies of crystals of organic and organometallic compounds by modern quantum chemical calculations within the framework of the densityfunctional theory reported in the last decade. Features of the software for such calculations are discussed. Examples of the use of quantum chemical calculations for the studies of the electronic structure, spectroscopic and other physicochemical properties of molecular crystals are presented. The bibliography includes 223 references.

A new approach for computing the atom-in-molecule [quantum theory of atoms in molecule (QTAIM)] energies in Kohn-Sham density-functional theory is presented and tested by computing QTAIM energies for a set of representative molecules. In the new approach, the contribution for the correlation-kinetic

Gallic acid (GA) is known by its antioxidant, anticarcinogenic properties and scavenger activity against several types of harmful free radicals. Molecularly imprinted polymers (MIPs) are used in separation of a pure compound from complex matrices. A stable template-monomer complex generates the MIPs with the highest affinity and selectivity for the template. The quantum chemical computations based on densityfunctional theory (DFT) was used on the template Gallic acid (GA), monomer acrylic acid (AA) and GA-AA complex to study the nature of interactions involved in the GA-AA complex. B3LYP/6-31+G(2d,2p) model chemistry was used to optimize their structures and frequency calculations. The effect of porogen acetonitrile (ACN) on complex formation was included by using polarizable continuum model (PCM). The results demonstrated the formation of a stable GA-AA complex through the intermolecular hydrogen bonding between carboxylic acid groups of GA and AA. The Mulliken atomic charge analysis and simulated vibrational spectra also supported the stable hydrogen bonding interaction between the carboxylic acid groups of GA and AA with minimal interference of porogen ACN. Further, simulations on GA-AA mole ratio revealed that 1:4 GA-AA was optimum for synthesis of MIP for GA.

Densityfunctional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.

Full Text Available Cysteine protease enzymes are important for human physiology and catalyze key protein degradation pathways. These enzymes react via a nucleophilic reaction mechanism that involves a cysteine residue and the proton of a proximal histidine. Particularly efficient inhibitors of these enzymes are nitrile-based, however, the details of the catalytic reaction mechanism currently are poorly understood. To gain further insight into the inhibition of these molecules, we have performed a combined densityfunctional theory and quantum mechanics/molecular mechanics study on the reaction of a nitrile-based inhibitor with the enzyme active site amino acids. We show here that small perturbations to the inhibitor structure can have dramatic effects on the catalysis and inhibition processes. Thus, we investigated a range of inhibitor templates and show that specific structural changes reduce the inhibitory efficiency by several orders of magnitude. Moreover, as the reaction takes place on a polar surface, we find strong differences between the DFT and QM/MM calculated energetics. In particular, the DFT model led to dramatic distortions from the starting structure and the convergence to a structure that would not fit the enzyme active site. In the subsequent QM/MM study we investigated the use of mechanical versus electronic embedding on the kinetics, thermodynamics and geometries along the reaction mechanism. We find minor effects on the kinetics of the reaction but large geometric and thermodynamics differences as a result of inclusion of electronic embedding corrections. The work here highlights the importance of model choice in the investigation of this biochemical reaction mechanism.

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of densityfunctionals.

In a paper on arXiv, Bonitz et al (2012 arXiv:1205.4922v1 [physics.plasm-ph]) (hereafter referred to as BPS) erroneously attributed the qualitative discrepancy between their densityfunctional theory (DFT) simulation results with the analytical discovery of the Shukla-Eliasson (SE) attractive force which brings ions closer to the failure of the linearized quantum hydrodynamic theory. In this paper, we describe the underlying physics of the novel SE attractive force and its validity, as well as discuss some of the key features of the well-established quantum hydrodynamic theory and working mechanisms for DFT simulations, in addition to giving some critical notes on the falsified and misleading conclusions presented by BPS in their dubious paper. Furthermore, we also present a mass-density value for possible 4He metallic plasma lattice formation under the SE force.

In a paper on arXiv, Bonitz et al (2012 arXiv:1205.4922v1 [physics.plasm-ph]) (hereafter referred to as BPS) erroneously attributed the qualitative discrepancy between their densityfunctional theory (DFT) simulation results with the analytical discovery of the Shukla-Eliasson (SE) attractive force which brings ions closer to the failure of the linearized quantum hydrodynamic theory. In this paper, we describe the underlying physics of the novel SE attractive force and its validity, as well as discuss some of the key features of the well-established quantum hydrodynamic theory and working mechanisms for DFT simulations, in addition to giving some critical notes on the falsified and misleading conclusions presented by BPS in their dubious paper. Furthermore, we also present a mass-density value for possible 4 He metallic plasma lattice formation under the SE force.

This chapter gives an introduction to first-principles electronic structure calculations based on the densityfunctional theory (DFT). Electronic structure calculations have a crucial importance in the multi-scale modelling scheme of materials: not only do they enable one to accurately determine physical and chemical properties of materials, they also provide data for the adjustment of parameters (or potentials) in higher-scale methods such as classical molecular dynamics, kinetic Monte Carlo, cluster dynamics, etc. Most of the properties of a solid depend on the behaviour of its electrons, and in order to model or predict them it is necessary to have an accurate method to compute the electronic structure. DFT is based on quantum theory and does not make use of any adjustable or empirical parameter: the only input data are the atomic number of the constituent atoms and some initial structural information. The complicated many-body problem of interacting electrons is replaced by an equivalent single electron problem, in which each electron is moving in an effective potential. DFT has been successfully applied to the determination of structural or dynamical properties (lattice structure, charge density, magnetisation, phonon spectra, etc.) of a wide variety of solids. Its efficiency was acknowledged by the attribution of the Nobel Prize in Chemistry in 1998 to one of its authors, Walter Kohn. A particular attention is given in this chapter to the ability of DFT to model the physical properties of nuclear materials such as actinide compounds. The specificities of the 5f electrons of actinides will be presented, i.e., their more or less high degree of localisation around the nuclei and correlations. The limitations of the DFT to treat the strong 5f correlations are one of the main issues for the DFT modelling of nuclear fuels. Various methods that exist to better treat strongly correlated materials will finally be presented. (author)

Using a simple relation of the Dirac delta-function to generalized the theta-function, the relationship between the tomographic probability approach and the quantum probability measure approach with the description of quantum states is discussed. The quantum state tomogram expressed in terms of the

Evolution of the helium atom in a strong time-dependent (TD) magnetic field (B) of strength up to 10 11 G is investigated through a quantum fluid dynamics (QFD) based current-densityfunctional theory (CDFT). The TD-QFD-CDFT computations are performed through numerical solution of a single generalized nonlinear Schroedinger equation employing vector exchange-correlation potentials and scalar exchange-correlation densityfunctionals that depend both on the electronic charge-density and the current-density. The results are compared with that obtained from a B-TD-QFD-DFT approach (based on conventional TD-DFT) under similar numerical constraints but employing only scalar exchange-correlation potential dependent on electronic charge-density only. The B-TD-QFD-DFT approach, at a particular TD magnetic field-strength, yields electronic charge- and current-densities as well as exchange-correlation potential resembling with that obtained from the time-independent studies involving static (time-independent) magnetic fields. However, TD-QFD-CDFT electronic charge- and current-densities along with the exchange-correlation potential and energy differ significantly from that obtained using B-TD-QFD-DFT approach, particularly at field-strengths >10 9 G, representing dynamical effects of a TD field. The work concludes that when a helium atom is subjected to a strong TD magnetic field of order >10 9 G, the conventional TD-DFT based approach differs 'dynamically' from the CDFT based approach under similar computational constraints. (author)

Full Text Available This research aims i to determine the density profile and calculate the ground state energy of a quantum dot in two dimensions (2D with a harmonic oscillator potential using orbital-free densityfunctional theory, and ii to understand the effect of the harmonic oscillator potential strength on the electron density profiles in the quantum dot. This study determines the total energy functional of the quantum dot that is a functional of the density that depends only on spatial variables. The total energy functional consists of three terms. The first term is the kinetic energy functional, which is the Thomas–Fermi approximation in this case. The second term is the external potential. The harmonic oscillator potential is used in this study. The last term is the electron–electron interactions described by the Coulomb interaction. The functional is formally solved to obtain the electron density as a function of spatial variables. This equation cannot be solved analytically, and thus a numerical method is used to determine the profile of the electron density. Using the electron density profiles, the ground state energy of the quantum dot in 2D can be calculated. The ground state energies obtained are 2.464, 22.26, 90.1957, 252.437, and 496.658 au for 2, 6, 12, 20, and 56 electrons, respectively. The highest electron density is localized close to the middle of the quantum dot. The density profiles decrease with the increasing distance, and the lowest density is at the edge of the quantum dot. Generally, increasing the harmonic oscillator potential strength reduces the density profiles around the center of the quantum dot.

The Hohenberg-Kohn theorem and Kohn-Sham procedure are extended to functionals of the localized intrinsic density of a self-bound system such as a nucleus. After defining the intrinsic-densityfunctional, we modify the usual Kohn-Sham procedure slightly to evaluate the mean-field approximation to the functional, and carefully describe the construction of the leading corrections for a system of fermions in one dimension with a spin-degeneracy equal to the number of particles N. Despite the fact that the corrections are complicated and nonlocal, we are able to construct a local Skyrme-like intrinsic-densityfunctional that, while different from the exact functional, shares with it a minimum value equal to the exact ground-state energy at the exact ground-state intrinsic density, to next-to-leading order in 1/N. We briefly discuss implications for real Skyrme functionals

Jul 27, 2017 ... a key role in all optical switching devices, since their optical properties can be .... optimized in the gas phase using DensityFunctional Theory. (DFT).39 The ...... The Mediation of Electrostatic Effects by Sol- vents J. Am. Chem.

We benchmark the ground state energies and the density profiles of atomic repulsive Fermi gases in optical lattices (OLs) computed via densityfunctional theory (DFT) against the results of diffusion Monte Carlo (DMC) simulations. The main focus is on a half-filled one-dimensional OLs, for which the DMC simulations performed within the fixed-node approach provide unbiased results. This allows us to demonstrate that the local spin-density approximation (LSDA) to the exchange-correlation functional of DFT is very accurate in the weak and intermediate interactions regime, and also to underline its limitations close to the strongly-interacting Tonks-Girardeau limit and in very deep OLs. We also consider a three-dimensional OL at quarter filling, showing also in this case the high accuracy of the LSDA in the moderate interaction regime. The one-dimensional data provided in this study may represent a useful benchmark to further develop DFT methods beyond the LSDA and they will hopefully motivate experimental studies to accurately measure the equation of state of Fermi gases in higher-dimensional geometries. Supplementary material in the form of one pdf file available from the Journal web page at http://https://doi.org/10.1140/epjb/e2018-90021-1.

The limitation on the size of quantum computers makes it important to reuse qubits for auxiliary registers even though they are entangled with others and are occupied by other computational processes. We construct a quantum algorithm that performs the functional phase rotation, which is the generalized form of the conventional conditional phase transforms, using the functional evaluation oracle. The constructed algorithm works without any a priori knowledge of the state of an auxiliary register at the beginning and it recovers the initial state of an auxiliary register at the end. This provides ample scope to choose qubits for auxiliary registers at will. (author)

Analytical expressions are given for the static structure factor S(k) and the pair correlation function g(r) for uniform ideal Bose-Einstein and Fermi-Dirac gases for all temperatures. In the vicinity of Bose Einstein condensation (BEC) temperature, g(r) becomes long ranged and remains so in the condensed phase. In the dilute gas limit, g(r) of bosons and fermions do not coincide with Maxwell-Boltzmann gas but exhibit bunching and anti-bunching effect respectively. The width of these functions depends on the temperature and is scaled as √(inverse atomic mass). Our numerical results provide the precise quantitative values of suppression/increase (antibunching and bunching) of the density fluctuations at small distances in ideal quantum gases in qualitative agreement with the experimental observation for almost non-trapped dilute gases.

We present a comparative study of the spatial distribution of the spin density of the ground state of CuCl2 using DensityFunctional Theory (DFT), quantum Monte Carlo (QMC), and post-Hartree-Fock wave function theory (WFT). A number of studies have shown that an accurate description of the electronic structure of the lowest-lying states of this molecule is particularly challenging due to the interplay between the strong dynamical correlation effects in the 3d shell and the delocalization of the 3d hole over the chlorine atoms. More generally, this problem is representative of the difficulties encountered when studying open-shell metal-containing molecular systems. Here, it is shown that qualitatively different results for the spin density distribution are obtained from the various quantum-mechanical approaches. At the DFT level, the spin density distribution is found to be very dependent on the functional employed. At the QMC level, Fixed-Node Diffusion Monte Carlo (FN-DMC) results are strongly dependent on the nodal structure of the trial wave function. Regarding wave function methods, most approaches not including a very high amount of dynamic correlation effects lead to a much too high localization of the spin density on the copper atom, in sharp contrast with DFT. To shed some light on these conflicting results Full CI-type (FCI) calculations using the 6-31G basis set and based on a selection process of the most important determinants, the so-called CIPSI approach (Configuration Interaction with Perturbative Selection done Iteratively) are performed. Quite remarkably, it is found that for this 63-electron molecule and a full CI space including about 10(18) determinants, the FCI limit can almost be reached. Putting all results together, a natural and coherent picture for the spin distribution is proposed.

A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent densityfunctional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.

This book deals with quantal densityfunctional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The treated time-independent QDFT constitutes a special case. In the 2nd edition, the theory is extended to include the presence of external magnetostatic fields. The theory is a description of matter based on the ‘quantal Newtonian’ first and second laws which is in terms of “classical” fields that pervade all space, and their quantal sources. The fields, which are explicitly defined, are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, correlation-kinetic, correlation-current-density, and correlation-magnetic effects. The book further describes Schrödinger theory from the new physical perspective of fields and quantal sources. It also describes traditional Hohenberg-Kohn-Sham DFT, and explains via QDFT the physics underlying the various energy functionals and functional derivatives o...

Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is diff...

The nonequilibrium description of quantum systems requires, for more than two or three particles, the use of a reduced description to be numerically tractable. Two possible approaches are based on either reduced density matrices or nonequilibrium Green functions (NEGF). Both concepts are formulated in terms of hierarchies of coupled equations—the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for the reduced density operators and the Martin-Schwinger-hierarchy (MS) for the Green functions, respectively. In both cases, similar approximations are introduced to decouple the hierarchy, yet still many questions regarding the correspondence of both approaches remain open. Here we analyze this correspondence by studying the generalized Kadanoff–Baym ansatz (GKBA) that reduces the NEGF to a single-time theory. Starting from the BBGKY-hierarchy we present the approximations that are necessary to recover the GKBA result both, with Hartree-Fock propagators (HF-GKBA) and propagators in second Born approximation. To test the quality of the HF-GKBA, we study the dynamics of a 4-electron Hubbard nanocluster starting from a strong nonequilibrium initial state and compare to exact results and the Wang-Cassing approximation to the BBGKY hierarchy presented recently by Akbari et al. [1].

A new Density-Functional formula is constructed for atoms. The kinetic energy of the electron is divided into two parts: the kinetic self-energy and the orthogonalization energy. Calculations were made for the total energies of neutral atoms, positive ions and for the He isoelectronic series. For neutral atoms the results match the Hartree-Fock energies within 1% for atoms with N 36 the results generally match the HF energies within 0.1%. For positive ions the results are fair; for the molecular applications a simplified model is developed in which the kinetic energy consists of the Weizsaecker term plus the Fermi energy reduced by a continuous function. (orig.) [de

A new Bayesian method for non-parametric density estimation is proposed, based on a mathematical analogy to quantum statistical physics. The mathematical procedure is related to maximum entropy methods for inverse problems and image reconstruction. The information divergence enforces global smoothing toward default models, convexity, positivity, extensivity and normalization. The novel feature is the replacement of classical entropy by quantum entropy, so that local smoothing is enforced by constraints on differential operators. The linear response of the estimate is proportional to the covariance. The hyperparameters are estimated by type-II maximum likelihood (evidence). The method is demonstrated on textbook data sets

Multicomponent densityfunctional theory (DFT) methods have been developed to treat two types of particles, such as electrons and nuclei, quantum mechanically at the same level. In the nuclear-electronic orbital (NEO) approach, all electrons and select nuclei, typically key protons, are treated quantum mechanically. For multicomponent DFT methods developed within the NEO framework, electron-proton correlation functionals based on explicitly correlated wavefunctions have been designed and used in conjunction with well-established electronic exchange-correlation functionals. Herein a general theory for multicomponent embedded DFT is developed to enable the accurate treatment of larger systems. In the general theory, the total electronic density is separated into two subsystem densities, denoted as regular and special, and different electron-proton correlation functionals are used for these two electronic densities. In the specific implementation, the special electron density is defined in terms of spatially localized Kohn-Sham electronic orbitals, and electron-proton correlation is included only for the special electron density. The electron-proton correlation functional depends on only the special electron density and the proton density, whereas the electronic exchange-correlation functional depends on the total electronic density. This scheme includes the essential electron-proton correlation, which is a relatively local effect, as well as the electronic exchange-correlation for the entire system. This multicomponent DFT-in-DFT embedding theory is applied to the HCN and FHF{sup −} molecules in conjunction with two different electron-proton correlation functionals and three different electronic exchange-correlation functionals. The results illustrate that this approach provides qualitatively accurate nuclear densities in a computationally tractable manner. The general theory is also easily extended to other types of partitioning schemes for multicomponent systems.

The magnetic properties of a new family of single-molecule magnet Ni(3)Mn(2) complexes were studied using theoretical methods based on DensityFunctional Theory (DFT). The first part of this study is devoted to analysing the exchange coupling constants, focusing on the intramolecular as well as the intermolecular interactions. The calculated intramolecular J values were in excellent agreement with the experimental data, which show that all the couplings are ferromagnetic, leading to an S = 7 ground state. The intermolecular interactions were investigated because the two complexes studied do not show tunnelling at zero magnetic field. Usually, this exchange-biased quantum tunnelling is attributed to the presence of intermolecular interactions calculated with the help of theoretical methods. The results indicate the presence of weak intermolecular antiferromagnetic couplings that cannot explain the ferromagnetic value found experimentally for one of the systems. In the second part, the goal is to analyse magnetic anisotropy through the calculation of the zero-field splitting parameters (D and E), using DFT methods including the spin-orbit effect.

This book aims to provide a detailed introduction to the state-of-the-art covariant densityfunctional theory, which follows the Lorentz invariance from the very beginning and is able to describe nuclear many-body quantum systems microscopically and self-consistently. Covariant densityfunctional theory was introduced in nuclear physics in the 1970s and has since been developed and used to describe the diversity of nuclear properties and phenomena with great success. In order to provide an advanced and updated textbook of covariant densityfunctional theory for graduate students and nuclear physics researchers, this book summarizes the enormous amount of material that has accumulated in the field of covariant densityfunctional theory over the last few decades as well as the latest developments in this area. Moreover, the book contains enough details for readers to follow the formalism and theoretical results, and provides exhaustive references to explore the research literature.

We present a minimal nuclear energy densityfunctional (NEDF) called "SeaLL1" that has the smallest number of possible phenomenological parameters to date. SeaLL1 is defined by seven significant phenomenological parameters, each related to a specific nuclear property. It describes the nuclear masses of even-even nuclei with a mean energy error of 0.97 MeV and a standard deviation of 1.46 MeV , two-neutron and two-proton separation energies with rms errors of 0.69 MeV and 0.59 MeV respectively, and the charge radii of 345 even-even nuclei with a mean error ɛr=0.022 fm and a standard deviation σr=0.025 fm . SeaLL1 incorporates constraints on the equation of state (EoS) of pure neutron matter from quantum Monte Carlo calculations with chiral effective field theory two-body (NN ) interactions at the next-to-next-to-next-to leading order (N3LO) level and three-body (NNN ) interactions at the next-to-next-to leading order (N2LO) level. Two of the seven parameters are related to the saturation density and the energy per particle of the homogeneous symmetric nuclear matter, one is related to the nuclear surface tension, two are related to the symmetry energy and its density dependence, one is related to the strength of the spin-orbit interaction, and one is the coupling constant of the pairing interaction. We identify additional phenomenological parameters that have little effect on ground-state properties but can be used to fine-tune features such as the Thomas-Reiche-Kuhn sum rule, the excitation energy of the giant dipole and Gamow-Teller resonances, the static dipole electric polarizability, and the neutron skin thickness.

The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theorems in the space fractional quantum mechanics and generalize the densityfunctional theory to the fractional quantum mechanics. -- Highlights: → Thomas-Fermi model under the framework of fractional quantum mechanics is studied. → We show the validity of the HK theorems in the space fractional quantum mechanics. → The densityfunctional theory is generalized to the fractional quantum mechanics.

We study quantum analogs of clasical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space. (orig.)

These lectures are an elementary introduction to standard many-body techniques applied to the study of quantum fields at finite temperature and density: perturbative expansion, linear response theory, quasiparticles and their interactions, etc... We emphasize the usefulness of the imaginary time formalism in a wide class of problems, as opposed to many recent approaches based on real time. Properties of elementary excitations in an ultrarelativistic plasma at high temperature or chemical potential are discussed, and recent progresses in the study of the quark-gluon plasma are briefly reviewed

A new quantum mechanical notion - Conditional Density Matrix - is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of quantum systems into subsystems and reunifications of subsystems into new joint systems. Conditional Density Matrix assigns a quantum state to a subsystem of a composite system on condition that another part of the composite system is in some pure state

By means of a formal expansion of the partition function presumably valid at large baryon densities, the propagator of the quarks is expressed in terms of the gluon propagator. This result is interpreted as implying that correlations between quarks and gluons are unimportant at high enough density, so that a kind of mean-field approximation gives a very accurate description of the physical system

Quantum entropy function is a proposal for computing the entropy associated with the horizon of a black hole in the extremal limit, and is related via AdS/CFT correspondence to the dimension of the Hilbert space in a dual quantum mechanics. We show that in N = 4 supersymmetric string theories, quantum entropy function formalism naturally explains the origin of the subtle differences between the microscopic degeneracies of quarter BPS dyons carrying different torsion, i.e. different arithmetical properties. These arise from additional saddle points in the path integral - whose existence depends on the arithmetical properties of the black hole charges - constructed as freely acting orbifolds of the original AdS 2 x S 2 near horizon geometry. During this analysis we demonstrate that the quantum entropy function is insensitive to the details of the infrared cutoff used in the computation, and the details of the boundary terms added to the action. We also discuss the role of the asymptotic symmetries of AdS 2 in carrying out the path integral in the definition of quantum entropy function. Finally we show that even though quantum entropy function is expected to compute the absolute degeneracy in a given charge and angular momentum sector, it can also be used to compute the index. This can then be compared with the microscopic computation of the index.

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but be a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. It is further argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. The suggested new interpretation of the wave function provides a natural realistic

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states. Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled 'spins' which are elements of u(1,1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams

Full Text Available Abstract: We discuss the basic concepts of densityfunctional theory (DFT as applied to materials modeling in the microscopic, mesoscopic and macroscopic length scales. The picture that emerges is that of a single unified framework for the study of both quantum and classical systems. While for quantum DFT, the central equation is a one-particle Schrodinger-like Kohn-Sham equation, the classical DFT consists of Boltzmann type distributions, both corresponding to a system of noninteracting particles in the field of a density-dependent effective potential, the exact functional form of which is unknown. One therefore approximates the exchange-correlation potential for quantum systems and the excess free energy densityfunctional or the direct correlation functions for classical systems. Illustrative applications of quantum DFT to microscopic modeling of molecular interaction and that of classical DFT to a mesoscopic modeling of soft condensed matter systems are highlighted.

Full Text Available Quantum time correlation functions are often the principal objects of interest in experimental investigations of the dynamics of quantum systems. For instance, transport properties, such as diffusion and reaction rate coefficients, can be obtained by integrating these functions. The evaluation of such correlation functions entails sampling from quantum equilibrium density operators and quantum time evolution of operators. For condensed phase and complex systems, where quantum dynamics is difficult to carry out, approximations must often be made to compute these functions. We present a general scheme for the computation of correlation functions, which preserves the full quantum equilibrium structure of the system and approximates the time evolution with quantum-classical Liouville dynamics. Several aspects of the scheme are discussed, including a practical and general approach to sample the quantum equilibrium density, the properties of the quantum-classical Liouville equation in the context of correlation function computations, simulation schemes for the approximate dynamics and their interpretation and connections to other approximate quantum dynamical methods.

In this paper, we present a function package for to calculate quantum resource measures and dynamics of open systems. Our package includes common operators and operator lists, frequently-used functions for computing quantum entanglement, quantum correlation, quantum coherence, quantum Fisher information and dynamics in noisy environments. We briefly explain the functions of the package and illustrate how to use the package with several typical examples. We expect that this package is a useful tool for future research and education.

Today, quantum mechanical densityfunctional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of densityfunctional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school. (paper)

We extend the idea of the constrained-search variational method for the construction of wave-functionfunctionals ψ[χ] of functions χ. The search is constrained to those functions χ such that ψ[χ] reproduces the density ρ(r) while simultaneously leading to an upper bound to the energy. The functionals are thereby normalized and automatically satisfy the electron-nucleus coalescence condition. The functionals ψ[χ] are also constructed to satisfy the electron-electron coalescence condition. The method is applied to the ground state of the helium atom to construct functionals ψ[χ] that reproduce the density as given by the Kinoshita correlated wave function. The expectation of single-particle operators W=Σ i r i n , n=-2,-1,1,2, W=Σ i δ(r i ) are exact, as must be the case. The expectations of the kinetic energy operator W=-(1/2)Σ i ∇ i 2 , the two-particle operators W=Σ n u n , n=-2,-1,1,2, where u=|r i -r j |, and the energy are accurate. We note that the construction of such functionals ψ[χ] is an application of the Levy-Lieb constrained-search definition of densityfunctional theory. It is thereby possible to rigorously determine which functional ψ[χ] is closer to the true wave function.

An efficient and convenient method for predicting the crystalline densities of energetic materials was established based on the quantum chemical computations. Densityfunctional theory (DFT) with four different basis sets (6-31G**, 6-311G**, 6-31+G**, and 6-311++G**) and various semiempirical molecular orbital (MO) methods have been employed to predict the molecular volumes and densities of a series of energetic nitramines including acyclic, monocyclic, and polycyclic/cage molecules. The relationships between the calculated values and experimental data were discussed in detail, and linear correlations were suggested and compared at different levels. The calculation shows that if the selected basis set is larger, it will expend more CPU (central processing unit) time, larger molecular volume and smaller density will be obtained. And the densities predicted by the semiempirical MO methods are all systematically larger than the experimental data. In comparison with other methods, B3LYP/6-31G** is most accurate and economical to predict the solid-state densities of energetic nitramines. This may be instructive to the molecular designing and screening novel HEDMs

In a recent paper (Shukla et al 2013 Phys. Scr. 87 018202) the authors criticized our analysis of the screened proton potential in dense hydrogen that was based on ab initio densityfunctional theory (DFT) simulations (Bonitz et al 2013 Phys. Rev. E 87 037102). In particular, they attributed the absence of the Shukla-Eliasson attractive force between protons in the DFT simulations to a failure of DFT. Here we discuss in detail their arguments and show that their conclusions are incorrect.

A quantum coherent switch having a substrate formed from a density wave (DW) material capable of having a periodic electron density modulation or spin density modulation, a dielectric layer formed onto a surface of the substrate that is orthogonal to an intrinsic wave vector of the DW material; and structure for applying an external spatially periodic electrostatic potential over the dielectric layer.

DensityFunctional Theory (DFT) has firmly established itself as the workhorse for the atomic-level simulation of condensed matter phases, pure or composite materials and quantum chemical systems. The present book is a rigorous and detailed introduction to the foundations up to and including such advanced topics as orbital-dependent functionals and both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, this text concentrates on the self-contained presentation of the basics of the most widely used DFT variants. This implies a thorough discussion of the corresponding existence theorems and effective single particle equations, as well as of key approximations utilized in implementations. The formal results are complemented by selected quantitative results, which primarily aim at illustrating strengths and weaknesses of a particular approach or functional. DFT for superconducting or nuclear and hadronic systems are not addressed in this work. The structure and material contain...

The sensing of external fields using quantum systems is a prime example of an emergent quantum technology. Generically, the sensitivity of a quantum sensor consisting of N independent particles is proportional to sqrt[N]. However, interactions invariably occurring at high densities lead to a breakdown of the assumption of independence between the particles, posing a severe challenge for quantum sensors operating at the nanoscale. Here, we show that interactions in quantum sensors can be transformed from a nuisance into an advantage when strong interactions trigger a dissipative phase transition in an open quantum system. We demonstrate this behavior by analyzing dissipative quantum sensors based upon nitrogen-vacancy defect centers in diamond. Using both a variational method and a numerical simulation of the master equation describing the open quantum many-body system, we establish the existence of a dissipative first order transition that can be used for quantum sensing. We investigate the properties of this phase transition for two- and three-dimensional setups, demonstrating that the transition can be observed using current experimental technology. Finally, we show that quantum sensors based on dissipative phase transitions are particularly robust against imperfections such as disorder or decoherence, with the sensitivity of the sensor not being limited by the T_{2} coherence time of the device. Our results can readily be applied to other applications in quantum sensing and quantum metrology where interactions are currently a limiting factor.

The sensing of external fields using quantum systems is a prime example of an emergent quantum technology. Generically, the sensitivity of a quantum sensor consisting of N independent particles is proportional to √{N }. However, interactions invariably occurring at high densities lead to a breakdown of the assumption of independence between the particles, posing a severe challenge for quantum sensors operating at the nanoscale. Here, we show that interactions in quantum sensors can be transformed from a nuisance into an advantage when strong interactions trigger a dissipative phase transition in an open quantum system. We demonstrate this behavior by analyzing dissipative quantum sensors based upon nitrogen-vacancy defect centers in diamond. Using both a variational method and a numerical simulation of the master equation describing the open quantum many-body system, we establish the existence of a dissipative first order transition that can be used for quantum sensing. We investigate the properties of this phase transition for two- and three-dimensional setups, demonstrating that the transition can be observed using current experimental technology. Finally, we show that quantum sensors based on dissipative phase transitions are particularly robust against imperfections such as disorder or decoherence, with the sensitivity of the sensor not being limited by the T2 coherence time of the device. Our results can readily be applied to other applications in quantum sensing and quantum metrology where interactions are currently a limiting factor.

The structure of the complexes of the type [Ni(L)(H(2)O)(2)](2+), where L is an amino alcohol ligand, L = N,N'-bis(2-hydroxyethyl)-ethane-1,2-diamine (BHEEN), N,N'-bis(2-hydroxycyclohexyl)-ethane-1,2-diamine (Cy(2)EN), and N,N'-bis(2-hydroxycyclopentyl)-ethane-1,2-diamine, (Cyp(2)EN) were investigated at the X3LYP/6-31+G(d,p) level of theory both in the gas phase and in solvent (CPCM model) to gain insight into factors that control the experimental log K(1) values. We find that (i) analyses based on Bader's quantum theory of atoms in molecules (QTAIM) are useful in providing significant insight into the nature of metal-ligand bonding and in clarifying the nature of weak "nonbonded" interactions in these complexes and (ii) the conventional explanation of complex stability in these sorts of complexes (based on considerations of bond lengths, bite angles and H-clashes) could be inadequate and indeed might be misleading. The strength of metal-ligand bonds follows the order Ni-N > Ni-OH ≥ Ni-OH(2); the bonds are predominantly ionic with some covalent character decreasing in the order Ni-N > Ni-OH > Ni-OH(2), with Ni-OH(2) being close to purely ionic. We predict that the cis complexes are preferred over the trans complexes because of (i) stronger bonding to the alcoholic O-donor atoms and (ii) more favorable intramolecular interactions, which appear to be important in determining the conformation of a metal-ligand complex. We show that (i) the flexibility of the ligand, which controls the Ni-OH bond length, and (ii) the ability of the ligand to donate electron density to the metal are likely to be important factors in determining values of log K(1). We find that the electron density at the ring critical point of the cyclopentyl moieties in Cyp(2)EN is much higher than that in the cyclohexyl moieties of Cy(2)EN and interpret this to mean that Cyp(2)EN is a poorer donor of electron density to a Lewis acid than Cy(2)EN.

Densityfunctional theory studies were conducted to determine an influence of the carrier concentration on the optical and electronic properties of InN/GaN superlattice system. The oscillator strength values, energy gaps and the band profiles were obtained. The band profiles were found to be strongly affected for technically possible heavy n-type doping while for p-type doping the carrier influence, both screening and band shift, is negligible. Blue shift of the transition energy between conduction band minima and valence band maxima was observed for high concentrations of both type carriers.

In a recent paper (Shukla et al 2013 Phys. Scr. 87 018202) the authors criticized our analysis of the screened proton potential in dense hydrogen that was based on ab initio densityfunctional theory (DFT) simulations (Bonitz et al 2013 Phys. Rev. E 87 037102). In particular, they attributed the absence of the Shukla–Eliasson attractive force between protons in the DFT simulations to a failure of DFT. Here we discuss in detail their arguments and show that their conclusions are incorrect. (comment)

The densityfunctional theory of nuclei has come to draw attention of scientists in the field of nuclear structure because the theory is expected to provide reliable numerical data in wide range on the nuclear chart. This article is organized to present an overview of the theory to the people engaged in the theory of other fields as well as those people in the nuclear physics experiments. At first, the outline of the densityfunctional theory widely used in the electronic systems (condensed matter, atoms, and molecules) was described starting from the Kohn-Sham equation derived on the variational principle. Then the theory used in the field of nuclear physics was presented. Hartree-Fock and Hartree-Fock-Bogolyubov approximation by using Skyrme interaction was explained. Comparison of the results of calculations and experiments of binding energies and ground state mean square charge radii of some magic number nuclei were shown. The similarity and dissimilarity between the two streams were summarized. Finally the activities of the international project of Universal Nuclear Energy DensityFunctional (UNEDF) which was started recently lead by US scientist was reported. This project is programmed for five years. One of the applications of the project is the calculation of the neutron capture cross section of nuclei on the r-process, which is absolutely necessary for the nucleosynthesis research. (S. Funahashi)

The non-collinear and collinear descriptions within relativistic densityfunctional theory is described. We present results of both non-collinear and collinear calculations for atoms, diatomic molecules, and some surface simulations. We find that the accuracy of our densityfunctional calculations for the smaller systems is comparable to good quantum chemical calculations, and thus this method provides a sound basis for larger systems where no such comparison is possible. (author)

Density fluctuations due Raman forward scattering (RFS) is analysed in the interaction of a high intensity laser pulse with high densityquantum plasma. The interaction model is developed using the quantum hydrodynamic (QHD) model which consist of a set of equations describing the transport of charge, density, momentum and energy of a charged particle system interacting through a self-consistent electrostatic potential. The nonlinear source current has been obtained incorporating the effects of quantum Bohm potential, Fermi pressure and electron spin. The laser spectrum is strongly modulated by the interaction, showing sidebands at the plasma frequency. Furthermore, as the quiver velocity of the electrons in the high electric field of the laser beam is quit large, various quantum effects are observed which can be attributed to the variation of electron mass with laser intensity.

By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of (ℎ/2π) 2 . In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when (ℎ/2π)→0.

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of DensityFunctional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg–Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb’s comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn–Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn–Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn–Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem

A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix (CDM). For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all the correlations between the two clusters. We show how to extract from the CDM a survey of the relative strengths of the system's correlations in different symmetry sectors and the nature of their decay with distance (power law or exponential), as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To achieve this goal, we introduce a new method of analysing the CDM, termed the dominant operator basis (DOB) method, which identifies in an unbiased fashion a small set of operators for each cluster that serve as a basis for the dominant correlations of the system. We illustrate this method by analysing the CDM for a spinless extended Hubbard model that features a competition between charge density correlations and pairing correlations, and show that the DOB method successfully identifies their relative strengths and dominant correlators. To calculate the ground state of this model, we use the density matrix renormalization group, formulated in terms of a variational matrix product state (MPS) approach within which subsequent determination of the CDM is very straightforward. In an extended appendix, we give a detailed tutorial introduction to our variational MPS approach for ground state calculations for one-dimensional quantum chain models. We present in detail how MPSs overcome the problem of large Hilbert space dimensions in these models and describe all the techniques needed for handling them in practice.

The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of densityfunctional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)

The present thesis is organized as follows. In Chapter 2 we study the Nucleon-Nucleon (NN) interaction in Dirac-Brueckner (DB) approach. We start by considering the NN interaction in free-space in terms of the Bethe-Salpeter (BS) equation to the meson exchange potential model. Then we present the DB approach for nuclear matter by extending the BS equation for the in-medium NN interaction. From the solution of the three-dimensional in-medium BS equation, we derive the DB self-energies and total binding energy which are the main results of the DB approach, which we later incorporate in the field theoretical calculation of the nuclear equation of state. In Chapter 3, we introduce the basic concepts of densityfunctional theory in the context of Quantum Hadrodynamics (QHD-I). We reach the main point of this work in Chapter 4 where we introduce the DDRH approach. In the DDRH theory, the medium dependence of the meson-nucleon vertices is expressed as functionals of the baryon field operators. Because of the complexities of the operator-valued functionals we decide to use the mean-field approximation. In Chapter 5, we contrast microscopic and phenomenological approaches to extracting density dependent meson-baryon vertices. Chapter 6 gives the results of our studies of the EOS of infinite nuclear matter in detail. Using formulas derived in Chapters 4 and 5 we calculate the properties of symmetric and asymmetric nuclear matter and pure neutron matter. (orig.)

We demonstrate the existence of different density-densityfunctionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard densityfunctional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized densityfunctional framework. The theory justifies and stimulates the search of optimal empirical densityfunctionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.

Chameleon fields are quantum (usually scalar) fields, with a density-dependent mass. In a high-density environment, the mass of the chameleon is large. On the contrary, in a small-density environment (e.g. on cosmological distances), the chameleon is very light. A model where the collapse of the wave function is induced by chameleon fields is presented. During this analysis, a Chameleonic Equivalence Principle (CEP) will be formulated: in this model, quantum gravitation is equivalent to a conformal anomaly. Further research efforts are necessary to verify whether this proposal is compatible with phenomeno logical constraints. (paper)

Itinerant density waves are model systems for studying quantum critical behavior. In both the model spin- and charge-density-wave systems Cr and NbSe2, it is possible to drive a continuous quantum phase transition with critical pressures below 10 GPa. Using x-ray diffraction techniques, we are able to directly track the evolution of the ordering wave vector Q across the pressure-temperature phase diagram. We find a non-monotonic dependence of Q on pressure. Using a Landau-Ginsburg theoretical framework developed by McMillan for CDWs, we evaluate the importance of the physical terms in driving the formation of ordered states at both the thermal and quantum phase transitions. We find that the itinerant instability is the deciding factor for the emergent order, which is further influenced by the critical fluctuations in both the thermal and quantum limits.

We study finite quantum wires and rings in the presence of a charge-density wave gap induced by a periodic modulation of the chemical potential. We show that the Tamm-Shockley bound states emerging at the ends of the wire are stable against weak disorder and interactions, for discrete open chains and for continuum systems. The low-energy physics can be mapped onto the Jackiw-Rebbi equations describing massive Dirac fermions and bound end states. We treat interactions via the continuum model and show that they increase the charge gap and further localize the end states. The electrons placed in the two localized states on the opposite ends of the wire can interact via exchange interactions and this setup can be used as a double quantum dot hosting spin qubits. The existence of these states could be experimentally detected through the presence of an unusual 4π Aharonov-Bohm periodicity in the spectrum and persistent current as a function of the external flux.

The possibility of implementing efficient (phase matched) HHG upconversion of deep- UV lasers in multiply-ionized plasmas, with potentially unprecedented conversion efficiency is a fascinating prospect. HHG results from the extreme nonlinear response of matter to intense laser light:high harmonics are radiated as a result of a quantum coherent electron recollision process that occurs during laser field ionization of an atom. Under current support from this grant in work published in Science in 2015, we discovered a new regime of bright HHG in highly-ionized plasmas driven by intense UV lasers, that generates bright harmonics to photon energies >280eV

We investigate the effects of shape and single-atom doping on the structural, optical absorption, Raman, and vibrational properties of Ag 13 , Ag 12 Cu 1 , Cu 13 , and Cu 12 Ag 1 clusters by using the (time-dependent) densityfunctional theory. The results show that the most stable structures are cuboctahedron (COh) for Ag 13 and icosahedron (Ih) for Cu 13 , Ag 12 Cu 1core , and Cu 12 Ag 1sur . In the visible—near infrared optical absorption, the transitions consist of the interband and the intraband transitions. Moreover, red shifts are observed as follows: 1) clusters change from Ag 12 Cu 1core to Ag 13 to Ag 12 Cu 1sur with the same motifs, 2) the shapes of pure Ag 13 and Ag 12 Cu 1core clusters change from COh to Ih to decahedron (Dh), 3) the shape of Ag 12 Cu 1sur clusters changes from Ih to COh to Dh, and 4) the shapes of pure Cu 13 and Cu 12 Ag 1 clusters change from Ih to Dh to COh. All of the Raman and vibrational spectra exhibit many significant vibrational modes related to the shapes and the compositions of the clusters. The ranges of vibrational spectra of Ag 13 , Ag 12 Cu 1 or Cu 13 , and Cu 12 Ag 1 clusters become narrower and the vibrational intensities increase as the shape of the clusters changes from Ih to Dh to COh. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

Full text: (author)Among numerous approaches to probabilistic interpretation of the conventional quantum mechanics the most close to the N. Bohr idea of the correspondence principle is the D.I. Blokhintzev - Ya.P. Terletsky approach using the quantum distribution function on the coordinate- momentum space. The detailed investigation of this approach has lead to the correspondence rule of V.V. Kuryshkin. Quantum mechanics of Kuryshkin (QMK) embody the program proposed by Yu.M. Shirokov for unifying classical and quantum mechanics in similar mathematical models. QMK develops and enhances Wigner's proposal concerning the calculation of quantum corrections to classical thermodynamic parameters using a phase distribution function. The main result of QMK is the possibility of description by mean of a positively-valued distribution function. This represents an important step towards a completely statistical model of quantum phenomena, compared with the quasi-probabilistic nature of Wigner distribution. Wigner's model does not permit to perform correctly the classical limit in quantum mechanics as well. On the other hand, QMK has a much more complex structure of operators of observables. One of the unsolved problems of QMK is the absence of a priori rules for establishing of auxiliary functions. Nevertheless, while it is impossible to overcome the complex form of operators, we find it quite possible to derive some methods of filing sets of auxiliary functions

We investigate entanglement and separability criteria of multipartite (n-partite) state by examining ranks of its reduced density matrices. Firstly, we construct the general formula to determine the criterion. A rank of origin density matrix always equals one, meanwhile ranks of reduced matrices have various ranks. Next, separability and entanglement criterion of multipartite is determined by calculating ranks of reduced density matrices. In this article we diversify multipartite state criteria into completely entangled state, completely separable state, and compound state, i.e. sub-entangled state and sub-entangledseparable state. Furthermore, we also shorten the calculation proposed by the previous research to determine separability of multipartite state and expand the methods to be able to differ multipartite state based on criteria above.

The problem on the distribution functions, leading to the similar local values of the particles number, pulse and energy, as in the quantum mechanics, is formulated and solved. The method is based on the quantum-mechanical determination of the probability density. The derived distribution function coincides with the Wigner function only for the spatial-homogeneous systems. The Bogolyubov equations chain, the Liouville equation for the distribution quantumfunctions by any number of particles in the system, the general expression for the tensor of the dielectric permittivity of the plasma electron component are obtained [ru

In this paper, we derived a Lorentz-covariant quantum Liouville equation for the density operator which describes the relativistic-quantum-information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced density operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of the nonrelativistic case, which is valid only in some specified reference frame. To show that our formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and could be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics

We study QCD with nonzero chemical potential on 4 4 lattices by averaging over the canonical partition functions, or sectors with fixed quark number. We derive a condensed matrix of size 2x3xL 3 whose eigenvalues can be used to find the canonical partition functions. We also experiment with a weight for configuration generation which respects the Z(3) symmetry which forces the canonical partition function to be zero for quark numbers that are not multiples of three. (orig.)

Any two-level quantum system can be used as a quantum bit (qubit) - the basic element of all devices and systems for quantum information and quantum computation. Recently it was proposed to study the strongly coupled system consisting of a two-level quantum dot and a monoenergetic photon gas in a microcavity-the strongly coupled quantum dot-microcavity (QD-MC) system for short, with the Jaynes-Cumming total Hamiltonian, for the application in the quantum information processing. Different approximations were applied in the theoretical study of this system. In this work, on the basis of the exact solution of the Schrodinger equation for this system without dissipation we derive the exact formulae for its density matrix. The realization of a qubit in this system is discussed. The solution of the system of rate equation for the strongly coupled QD-MC system in the presence of the interaction with the environment was also established in the first order approximation with respect to this interaction.

The report describes research in theoretical quantum chromodynamics, including effective field theories of hadronic interactions, properties of strongly interacting matter at extreme energy density, phenomenology of relativistic heavy ion collisions, and algorithms and numerical simulations of lattice gauge theory and other many-body systems.

The report describes research in theoretical quantum chromodynamics, including effective field theories of hadronic interactions, properties of strongly interacting matter at extreme energy density, phenomenology of relativistic heavy ion collisions, and algorithms and numerical simulations of lattice gauge theory and other many-body systems.

Quantum embedding theory aims to provide an efficient solution to obtain accurate electronic energies for systems too large for full-scale, high-level quantum calculations. It adopts a hierarchical approach that divides the total system into a small embedded region and a larger environment, using different levels of theory to describe each part. Previously, we developed a density-based quantum embedding theory called densityfunctional embedding theory (DFET), which achieved considerable success in metals and semiconductors. In this work, we extend DFET into a density-matrix-based nonlocal form, enabling DFET to study the stronger quantum couplings between covalently bonded subsystems. We name this theory density-matrix functional embedding theory (DMFET), and we demonstrate its performance in several test examples that resemble various real applications in both chemistry and biochemistry. DMFET gives excellent results in all cases tested thus far, including predicting isomerization energies, proton transfer energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps for local chromophores. Here, we show that DMFET systematically improves the quality of the results compared with the widely used state-of-the-art methods, such as the simple capped cluster model or the widely used ONIOM method.

Carbon linear atomic chains attached to graphene have experimentally been produced. Motivated by these results, we study the nature of the carbon bonds in these nanowires and how it affects their electrical properties. In the present study we investigate chains with different numbers of atoms and we observe that nanowires with odd number of atoms present a distinct behavior than the ones with even numbers. Using graphene nanoribbons as leads, we identify differences in the quantum transport of the chains with the consequence that even and odd numbered chains have low and high electrical conduction, respectively. We also noted a dependence of current with the wire size. We study this unexpected behavior using a combination of first principles calculations and simple models based on chemical bond theory. From our studies, the electrons of carbon nanowires present a quasi-free electron behavior and this explains qualitatively the high electrical conduction and the bond lengths with unexpected values for the case of odd nanowires. Our study also allows the understanding of the electric conduction dependence with the number of atoms and their parity in the chain. In the case of odd number chains a proposed π-bond (MpB) model describes unsaturated carbons that introduce a mobile π-bond that changes dramatically the structure and transport properties of these wires. Our results indicate that the nature of bonds plays the main role in the oscillation of quantum electrical conduction for chains with even and odd number of atoms and also that nanowires bonded to graphene nanoribbons behave as a quasi-free electron system, suggesting that this behavior is general and it could also remain if the chains are bonded to other materials

Full Text Available We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.

We compare several definitions of the density of a self-bound system, such as a nucleus, in relation with its center-of-mass zero-point motion. A trivial deconvolution relates the internal density to the density defined in the laboratory frame. This result is useful for the practical definition of densityfunctionals

The trajectory-density method of a quantum system is developed by using local Koopman and Frobenius–Perron operators. We propose a new scheme of approximation from two sets of trajectory-density mixed equations. By examining the local generation and termination of trajectories, we show how they can be adopted to the propagation of negative values of the Wigner function even if it starts off positive everywhere

In this article, we report the characterization of novel oligothienoacenes with five and seven fused thiophene rings, materials with potential applications in organic electronics. In contrast to usual alpha-linked oligothiophenes, these fused oligothiophenes have a larger band gap than most semiconductors currently used in the fabrication of organic field-effect transistors (OFETs) and therefore they are expected to be more stable in air. The synthesis of these fused-ring oligomers was motivated by the notion that a more rigid and planar structure should reduce defects (such as torsion about single bonds between alpha-linked units or S-syn defects) and thus improve conjugation for better charge-carrier mobility. The conjugational properties of these two molecular materials have been investigated by means of FT-Raman spectroscopy, revealing that conjugation still increases in passing from the five-ring oligomer to that with seven-rings. DFT and TDDFT quantum chemical calculations have been performed, at the B3LYP/6-31G level, to assess information regarding the minimum-energy molecular structure, topologies, and absolute energies of the frontier molecular orbitals (MOs.) around the gap, vibrational normal modes related to the main Raman features, and vertical one-electron excitations giving rise to the main optical absorptions.

Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized

We employ detuning-dependent decay-rate measurements of a quantum dot in a photonic-crystal cavity to study the influence of phonon dephasing in a solid-state quantum-electrodynamics experiment. The experimental data agree with a microscopic non-Markovian model accounting for dephasing from...... longitudinal acoustic phonons, and the analysis explains the difference between nonresonant cavity feeding in different nanocavities. From the comparison between experiment and theory we extract the effective phonon density of states experienced by the quantum dot in the nanocavity. This quantity determines...

The authors demonstrate a method for obtaining the ground state energies and charge densities of a system of atoms described within densityfunctional theory using simulated annealing on a parallel computer

Quantum chemical techniques such as densityfunctional theory (DFT) have become a powerful tool in the investigation of the molecular structure and vibrational spectrum and are finding increasing use in application related to biological systems. The Fourier transform infrared (FT-IR) and Fourier transform Raman (FT-Raman) techniques are employed to characterize the title compound. The vibrational frequencies were obtained by DFT/B3LYP calculations with 6-31G(d,p) and 6-311 ++G(d,p) as basis sets. The geometry of the title compound was optimized. The vibrational assignments and the calculation of Potential Energy Distribution (PED) were carried out using the Vibrational Energy Distribution Analysis (VEDA) software. Molecular electrostatic potential was calculated for the title compound to predict the reactive sites for electrophilic and nucleophilic attack. In addition, the first-order hyperpolarizability, HOMO and LUMO energies, Fukui function and NBO were computed. The thermodynamic properties of the title compound were calculated at different temperatures, revealing the correlations between heat capacity (C), entropy (S) and enthalpy changes (H) with temperatures. Molecular docking studies were also conducted as part of this study. The paper further explains the experimental results which are in line with the theoretical calculations and provide optimistic evidence through molecular docking that the title compound can act as a good antidepressant. It also provides sufficient justification for the title compound to be selected as a good candidate for further studies related to NLO properties.

Complexes with pincer ligand moieties have garnered much attention in the past few decades. They have been shown to be highly active catalysts in several known transition metal-catalyzed organic reactions as well as some unprecedented organic transformations. At the same time, the use of computational organometallic chemistry to aid in the understanding of the mechanisms in organometallic catalysis for the development of improved catalysts is on the rise. While it was common in earlier studies to reduce computational cost by truncating donor group substituents on complexes such as tertbutyl or isopropyl groups to hydrogen or methyl groups, recent advancements in the processing capabilities of computer clusters and codes have streamlined the time required for calculations. As the full modeling of complexes become increasingly popular, a commonly overlooked aspect, especially in the case of complexes bearing isopropyl substituents, is the conformational analysis of complexes. Isopropyl groups generate a different conformer with each 120 ° rotation (rotamer), and it has been found that each rotamer typically resides in its own potential energy well in densityfunctional theory studies. As a result, it can be challenging to select the most appropriate structure for a theoretical study, as the adjustment of isopropyl substituents from a higher-energy rotamer to the lowest-energy rotamer usually does not occur during structure optimization. In this report, the influence of the arrangement of isopropyl substituents in pincer complexes on calculated complex structure energies as well as a case study on the mechanism of the isomerization of an iPrPCP-Fe complex is covered. It was found that as many as 324 rotamers can be generated for a single complex, as in the case of an iPrPCP-Ni formato complex, with the energy difference between the global minimum and the highest local minimum being as large as 16.5 kcalmol-1. In the isomerization of a iPrPCP-Fe complex, it was found

The purpose of this book is to give a systematic pedagogical exposition of the quantitative analysis of Wilson lines and gauge-invariant correlation functions in quantum chromodynamics. Using techniques from the previous volume (Wilson Lines in Quantum Field Theory, 2014), an ab initio methodology is developed and practical tools for its implementation are presented. Emphasis is put on the implications of gauge invariance and path-dependence properties of transverse-momentum dependent parton densityfunctions. The latter are associated with the QCD factorization approach to semi-inclusive hadronic processes, studied at currently operating and planned experimental facilities.

The purpose of this book is to give a systematic pedagogical exposition of the quantitative analysis of Wilson lines and gauge-invariant correlation functions in quantum chromodynamics. Using techniques from the previous volume (Wilson Lines in Quantum Field Theory, 2014), an ab initio methodology is developed and practical tools for its implementation are presented. Emphasis is put on the implications of gauge invariance and path-dependence properties of transverse-momentum dependent parton densityfunctions. The latter are associated with the QCD factorization approach to semi-inclusive hadronic processes, studied at currently operating and planned experimental facilities.

In this paper, we clarify the relation between Manin's quantum theta function and Schwarz's theta vector. We do this in comparison with the relation between the kq representation, which is equivalent to the classical theta function, and the corresponding coordinate space wavefunction. We first explain the equivalence relation between the classical theta function and the kq representation in which the translation operators of the phase space are commuting. When the translation operators of the phase space are not commuting, then the kq representation is no longer meaningful. We explain why Manin's quantum theta function, obtained via algebra (quantum torus) valued inner product of the theta vector, is a natural choice for the quantum version of the classical theta function. We then show that this approach holds for a more general theta vector containing an extra linear term in the exponent obtained from a holomorphic connection of constant curvature than the simple Gaussian one used in Manin's construction

In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called "discord density" can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.

LIBXC is a library of exchange-correlation functionals for density-functional theory. We are concerned with semi-local functionals (or the semi-local part of hybrid functionals), namely local-density approximations, generalized-gradient approximations, and meta-generalized-gradient approximations. Currently we include around 400 functionals for the exchange, correlation, and the kinetic energy, spanning more than 50 years of research. Moreover, LIBXC is by now used by more than 20 codes, not only from the atomic, molecular, and solid-state physics, but also from the quantum chemistry communities.

Isothioureas, inhibitors of nitric oxide synthases, have been studied experimentally in solid state by nuclear quadrupole double resonance (NQDR) and X-ray methods and theoretically by the quantum theory of atoms in molecules/densityfunctional theory. Resonance frequencies on (14)N have been detected and assigned to particular nitrogen sites in each molecule. The crystal packings of (S)-3,4-dichlorobenzyl-N-methylisothiouronium chloride with the disordered chlorine positions in benzene ring and (S)-butyloisothiouronium bromide have been resolved in X-ray diffraction studies. (14)N NQDR spectra have been found good indicators of isomer type and strength of intra- or intermolecular N-H···X (X = Cl, Br) interactions. From among all salts studied, only for (S)-2,3,4,5,6-pentabromobenzylisothiouronium chloride are both nitrogen sites equivalent, which has been explained by the slow exchange. This unique structural feature can be a key factor in the high biological activity of (S)-2,3,4,5,6-pentabromobenzylisothiouronium salts.

We derive systematic rules for calculating the imaginary parts of Minkowski space Green functions in quantum field theory at finite temperature and density. Self-energy corrections are used as an example of the application of these rules. (orig.)

Even the quantum simulation of an apparently simple molecule such as Fe2S2 requires a considerable number of qubits of the order of 106, while more complex molecules such as alanine (C3H7NO2) require about a hundred times more. In order to assess such a multimillion scale of identical qubits and control lines, the silicon platform seems to be one of the most indicated routes as it naturally provides, together with qubit functionalities, the capability of nanometric, serial, and industrial-quality fabrication. The scaling trend of microelectronic devices predicting that computing power would double every 2 years, known as Moore's law, according to the new slope set after the 32-nm node of 2009, suggests that the technology roadmap will achieve the 3-nm manufacturability limit proposed by Kelly around 2020. Today, circuital quantum information processing architectures are predicted to take advantage from the scalability ensured by silicon technology. However, the maximum amount of quantum information per unit surface that can be stored in silicon-based qubits and the consequent space constraints on qubit operations have never been addressed so far. This represents one of the key parameters toward the implementation of quantum error correction for fault-tolerant quantum information processing and its dependence on the features of the technology node. The maximum quantum information per unit surface virtually storable and controllable in the compact exchange-only silicon double quantum dot qubit architecture is expressed as a function of the complementary metal-oxide-semiconductor technology node, so the size scale optimizing both physical qubit operation time and quantum error correction requirements is assessed by reviewing the physical and technological constraints. According to the requirements imposed by the quantum error correction method and the constraints given by the typical strength of the exchange coupling, we determine the workable operation frequency

Recently, the progression toward more exact densityfunctional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a "path". Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and "straying" from the "path" by separating errors in ρ and E[ρ]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities ρ' can be used to estimate the significance of errors in ρ without knowing the exact densities which are often inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated using CCSD(T)/aug-cc-pV5Z as benchmark at chemical accuracy. Four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of the different ρ are energy-wise insignificant. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large "normal" problems such as the Co-C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ mol -1 in accuracy. The proposed method of using a test set of trial densities to estimate the sensitivity and significance of density errors of functionals may be useful for testing and designing new balanced functionals with more systematic improvement of densities and energies.

We discuss density of states functions for photonic crystals, in the context of the two-dimensional problem for arrays of cylinders of arbitrary cross section. We introduce the mutual density of states (MDOS), and show that this function can be used to calculate both the local density of states (LDOS), which gives position information for emission of radiation from photonic crystals, and the spectral density of states (SDOS), which gives angular information. We establish the connection between MDOS, LDOS, SDOS and the conventional density of states, which depends only on frequency. We relate all four functions to the band structure and propagating states within the crystal, and give numerical examples of the relation between band structure and density of states functions

We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the electron-electron interaction. This gives a straightforward extension ...

Of all the different areas in computational chemistry, densityfunctional theory (DFT) enjoys the most rapid development. Even at the level of the local density approximation (LDA), which is computationally less demanding, DFT can usually provide better answers than Hartree-Fock formalism for large systems such as clusters and solids. For atoms and molecules, the results from DFT often rival those obtained by ab initio quantum chemistry, partly because larger basis sets can be used. Such encouraging results have in turn stimulated workers to further investigate the formal theory as well as the

This paper gives an introduction to the technique of functional differentiation and integration in curved spacetime, applied to examples from quantum field theory. Special attention is drawn on the choice of functional integral measure. Referring to a suggestion by Toms, fields are choosen as arbitrary scalar, spinorial or vectorial densities. The technique developed by Toms for a pure quadratic Lagrangian are extended to the calculation of the generating functional with external sources. Included are two examples of interacting theories, a self-interacting scalar field and a Yang-Mills theory. For these theories the complete set of Feynman graphs depending on the weight of variables is derived. (orig.)

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field densityfunctional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local densityfunctionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.

A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field densityfunctional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local densityfunctionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules

We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, deriving vertex expansions and composition laws they satisfy. We clarify the tie between definitions using a group averaging procedure and those in a deparametrised framework. We draw some conclusions about the physics of a single quantum universe and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

In this work we show the possibility to extract Kohn-Sham orbitals, orbital energies, and exchange correlation potentials from accurate Quantum Monte Carlo (QMC) densities for atoms (He, Be, Ne) and molecules (H 2 , Be 2 , H 2 O, and C 2 H 4 ). The Variational Monte Carlo (VMC) densities based on accurate Jastrow Antisymmetrised Geminal Power wave functions are calculated through different estimators. Using these reference densities, we extract the Kohn-Sham quantities with the method developed by Zhao, Morrison, and Parr (ZMP) [Phys. Rev. A 50, 2138 (1994)]. We compare these extracted quantities with those obtained form CISD densities and with other data reported in the literature, finding a good agreement between VMC and other high-level quantum chemistry methods. Our results demonstrate the applicability of the ZMP procedure to QMC molecular densities, that can be used for the testing and development of improved functionals and for the implementation of embedding schemes based on QMC and DensityFunctional Theory

We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green's functions. The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.

Understanding the roles of the temporary and spatial structures of quantumfunctional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functionalquantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems

Recently, the progression toward more exact densityfunctional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a “path”. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness...

Based on the Hohenberg-Kohn lemma and the hypotheses of the densityfunctional existence for the external-field potential, it is shown that the strict result of the densityfunctional theory is the equation of the external-field potential as the densityfunctional. This result leads to the

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size.

Highlights: • The present work deals with the study of the electronic spectral density of electron pairs and its effect in charge transport in superconductor-quantum dot-superconductor junctions. • The charge transfer across such junctions can be controlled by changing the positions of the dot level. • The Josephson supercurrent can also be tuned by controlling the position of quantum dot energy levels. - Abstract: In the present paper, we report the role of quantum dot energy levels on the electronic spectral density for a two level quantum dot coupled to s-wave superconducting leads. The theoretical arguments in this work are based on the Anderson model so that it necessarily includes dot energies, single particle tunneling and superconducting order parameter for BCS superconductors. The expression for single particle spectral function is obtained by using the Green's function equation of motion technique. On the basis of numerical computation of spectral function of superconducting leads, it has been found that the charge transfer across such junctions can be controlled by the positions and availability of the dot levels.

We study the quantum theory of a simple general relativistic quantum model of two coupled harmonic oscillators and compute the two-point function following a proposal first introduced in the context of loop quantum gravity.

The Hohenberg-Kohn densityfunctional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to densityfunctional approximations. Analyzing highly accurate atomic correlation energies, we show that E{sub C} → −A{sub C} ZlnZ + B{sub C}Z as Z → ∞, where Z is the atomic number, A{sub C} is known, and we estimate B{sub C} to be about 37 mhartree. The local density approximation yields A{sub C} exactly, but a very incorrect value for B{sub C}, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of densityfunctional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with B{sub C} a functional of the TF density for the system. The implications for the construction of approximate densityfunctionals are discussed.

Background: The explicit density dependence in the coupling coefficients entering the nonrelativistic nuclear energy-densityfunctional (EDF) is understood to encode effects of three-nucleon forces and dynamical correlations. The necessity for the density-dependent coupling coefficients to assume the form of a preferably small fractional power of the density ρ is empirical and the power is often chosen arbitrarily. Consequently, precision-oriented parametrizations risk overfitting in the regime of saturation and extrapolations in dilute or dense matter may lose predictive power. Purpose: Beginning with the observation that the Fermi momentum kF, i.e., the cubic root of the density, is a key variable in the description of Fermi systems, we first wish to examine if a power hierarchy in a kF expansion can be inferred from the properties of homogeneous matter in a domain of densities, which is relevant for nuclear structure and neutron stars. For subsequent applications we want to determine a functional that is of good quality but not overtrained. Method: For the EDF, we fit systematically polynomial and other functions of ρ1 /3 to existing microscopic, variational calculations of the energy of symmetric and pure neutron matter (pseudodata) and analyze the behavior of the fits. We select a form and a set of parameters, which we found robust, and examine the parameters' naturalness and the quality of resulting extrapolations. Results: A statistical analysis confirms that low-order terms such as ρ1 /3 and ρ2 /3 are the most relevant ones in the nuclear EDF beyond lowest order. It also hints at a different power hierarchy for symmetric vs. pure neutron matter, supporting the need for more than one density-dependent term in nonrelativistic EDFs. The functional we propose easily accommodates known or adopted properties of nuclear matter near saturation. More importantly, upon extrapolation to dilute or asymmetric matter, it reproduces a range of existing microscopic

A path integral representation is derived for the Wigner distribution function of a nonequilibrium system coupled with heat bath. Under appropriate conditions, the Wigner distribution function approaches an equilibrium distribution, which manifests shifting and broadening of spectral lines due to the interaction with heat bath. It is shown that the equilibrium distribution becomes the quantum canonical distribution in the vanishing coupling constant limit. (author)

The cosmological constant problem is reanalyzed by imposing the limitation of the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the calculation of the energy density of a field theory. It is shown that if a quantum field theory has to be consistent with gravity and holography, i.e. with an upper limit of storing information in a given area, the ultraviolet momentum cut-off is not the Planck mass, M_p, as naively expected, but M_p/N_U^(1/4) where N_U is the number of ...

Starting with a brief introduction to excited-state densityfunctional theory, we present our method of constructing modified local density approximated (MLDA) energy functionals for the excited states. We show that these functionals give accurate results for kinetic energy and exchange energy compared to the ground state LDA functionals. Further, with the inclusion of GGA correction, highly accurate total energies for excited states are obtained. We conclude with a brief discussion on the further direction of research that include the construction of correlation energy functional and exchange potential for excited states.

We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results. (orig.)

Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of interacting electronic many-body systems formally exactly and in a practical and efficient manner. TDDFT has become the leading method for calculating excitation energies and optical properties of large molecules, with accuracies that rival traditional wave-function based methods, but at a fraction of the computational cost.This book is the first graduate-level text on the concepts and applications of TDDFT, including many examples and exercises, and extensive coverage of the literature. The book begins with a s

Study of nucleation and growth phenomena in condensation is of prime importance in various applications such as crystal growth, nanoparticle synthesis, pattern formation etc. The knowledge of nucleation barrier in condensation is necessary to control the nucleation kinetics, size of the nanoparticles etc. Classical nucleation theory (CNT) assumes the density of the drop as bulk density irrespective of the size of the drop and overestimates the nucleation barrier. Here we are interested in solving the problem analytically using densityfunctional theory (DFT) with square gradient approximation along the lines of Cahn and Hilliard. Nucleation barrier and density profile obtained in this work are consistent with other works based on nonclassical theory. (author)

We study a formulation of quantum mechanics in which the central notion is that of a quantum-mechanical history---a sequence of events at a succession of times. The primary aim is to identify sets of ''decoherent'' (or ''consistent'') histories for the system. These are quantum-mechanical histories suffering negligible interference with each other, and, therefore, to which probabilities may be assigned. These histories may be found for a given system using the so-called decoherence functional. When the decoherence functional is exactly diagonal, probabilities may be assigned to the histories, and all probability sum rules are satisfied exactly. We propose a condition for approximate decoherence, and argue that it implies that most probability sum rules will be satisfied to approximately the same degree. We also derive an inequality bounding the size of the off-diagonal terms of the decoherence functional. We calculate the decoherence functional for some simple one-dimensional systems, with a variety of initial states. For these systems, we explore the extent to which decoherence is produced using two different types of coarse graining. The first type of coarse graining involves imprecise specification of the particle's position. The second involves coupling the particle to a thermal bath of harmonic oscillators and ignoring the details of the bath (the Caldeira-Leggett model). We argue that both types of coarse graining are necessary in general. We explicitly exhibit the degree of decoherence as a function of the temperature of the bath, and of the width to within which the particle's position is specified. We study the diagonal elements of the decoherence functional, representing the probabilities for the possible histories of the system

An expansion of the energy functional in terms of the total number of electrons and the normal coordinates within the canonical ensemble is presented. A comparison of this expansion with the expansion of the energy in terms of the total number of electrons and the external potential leads to new relations among common densityfunctional reactivity descriptors. The formulas obtained provide explicit links between important quantities related to the chemical reactivity of a system. In particular, the relation between the nuclear and the electronic Fukui functions is recovered. The connection between the derivatives of the electronic energy and the nuclear repulsion energy with respect to the external potential offers a proof for the "Quantum Chemical le Chatelier Principle." Finally, the nuclear linear response function is defined and the relation of this function with the electronic linear response function is given.

We investigate low-density, quantum-degenerate gases in the presence of a localized attractive potential in the centre of a one-dimensional harmonic trap. The attractive potential is modelled using a parameterized δ-function, allowing us to determine all single-particle eigenfunctions analytically. From these we calculate the ground-state many-body properties for a system of spin-polarized fermions and, using the Bose-Fermi mapping theorem, extend the results to strongly interacting bosonic systems. We discuss the single-particle densities, the pair-correlation functions, the reduced single-particle density matrices and the momentum distributions as a function of the particle number and strength of the attractive point potential. As an important experimental observable, we place special emphasis on spatial coherence properties of such samples.

Expressions for the reduced matrices and densityfunctions of N-fermion systems of arbitrary order s (1<=s<=N) are derived within the frame of rigorous spin approach to the densityfunctional theory (DFT). Using the local-scale transformation method and taking into account the particle spin it is shown that the reduced matrices and densityfunctions are functionals of the total one-fermion density. Similar dependence is found for the distribution density of s-particle aggregates. Generalization and applicability of DFT to the case of s-particle ensembles and aggregates is discussed. 14 refs

We present a theoretical model to study spin injection (η) through a quantum dot system sandwiched by two ferromagnetic contacts. The effect of contact magnetization on η was studied using Green's function descriptions of the density of states. Green's function models have the advantages that coherent effects of temperature, electron occupation in the QD, and lead perturbation on the state wave function and hence the current can be formally included in the calculations. In addition, self-consistent treatment of current with applied electrochemical potential or lead conductivity, a necessary step which has not been considered in previous works, has also been implemented in our model

Theoretical chemistry has a paradox of choice due to the availability of a myriad of densityfunctionals and basis sets. Traditionally, a particular densityfunctional is chosen on the basis of the level of user expertise (i.e., subjective experiences). Herein we circumvent the user-centric selection procedure by describing a novel approach for objectively selecting a particular functional for a given application. We achieve this by employing game theory to identify optimal functional/basis set combinations. A three-player (accuracy, complexity, and similarity) game is devised, through which Nash equilibrium solutions can be obtained. This approach has the advantage that results can be systematically improved by enlarging the underlying knowledge base, and the deterministic selection procedure mathematically justifies the densityfunctional and basis set selections.

The main part of this book is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and bound-level information. The bound-level treatment gives a clear physical understanding of "difficult" questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book.

Time-dependent densityfunctional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn–Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn–Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn–Sham potential with controllable error bounds. (paper)

We study experimentally time-resolved emission of colloidal CdSe quantum dots in an environment with a controlled local density of states LDOS. The decay rate is measured versus frequency and as a function of distance to a mirror. We observe a linear relation between the decay rate and the LDOS, ...... with the measured radiative rates. Our results are relevant for applications of CdSe quantum dots in spontaneous emission control and cavity quantum electrodynamics.......We study experimentally time-resolved emission of colloidal CdSe quantum dots in an environment with a controlled local density of states LDOS. The decay rate is measured versus frequency and as a function of distance to a mirror. We observe a linear relation between the decay rate and the LDOS......, allowing us to determine the size-dependent quantum efficiency and oscillator strength. We find that the quantum efficiency decreases with increasing emission energy mostly due to an increase in nonradiative decay. We manage to obtain the oscillator strength of the important class of CdSe quantum dots...

A review of some recent advances in zeta function techniques is given, in problems of pure mathematical nature but also as applied to the computation of quantum vacuum fluctuations in different field theories, and specially with a view to cosmological applications

The solution of the square root of the Schroedinger equation for the supersymmetric quantum mechanics is expressed in the form of series. The formula may be considered as a functional integral of the chronological exponent of the super-pseudodifferential operator symbol over the superspace. 10 refs

Densityfunctional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy-to-computational c......Densityfunctional theory (DFT) emerged almost 50 years ago. Since then DFT has established itself as the central electronic structure methodology for simulating atomicscale systems from a few atoms to a few hundred atoms. This success of DFT is due to a very favorable accuracy...... resampling techniques, thereby systematically avoiding problems with overfitting. The first ever densityfunctional presenting both reliable accuracy and convincing error estimation is generated. The methodology is general enough to be applied to more complex functional forms with higher-dimensional fitting...

In this paper we present nonlocal kinetic-energy functionals T[n] within the average density approximation (ADA) framework, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system. In contrast with previous ADA functionals, these present good behavior of the long-range tail of the exact weight function. The averaging procedure for the kinetic functional (averaging the Fermi momentum of the electron gas, instead of averaging the electron density) leads to a functional without numerical difficulties in the calculation of extended systems, and it gives excellent results when applied to atoms and jellium surfaces. copyright 1996 The American Physical Society

Generally confinement size is considered to determine the dimensionality of nanostructures. While the exciton Bohr radius is used as a criterion to define either weak or strong confinement in optical experiments, the binding energy of confined excitons is difficult to measure experimentally. One alternative is to use the temperature dependence of the radiative recombination time, which has been employed previously in quantum wells and quantum wires. A one-dimensional loop structure is often assumed to model quantum rings, but this approximation ceases to be valid when the rim width becomes comparable to the ring radius. We have evaluated the density of states in a single quantum ring by measuring the temperature dependence of the radiative recombination of excitons, where the photoluminescence decay time as a function of temperature was calibrated by using the low temperature integrated intensity and linewidth. We conclude that the quasi-continuous finely-spaced levels arising from the rotation energy give rise to a quasi-one-dimensional density of states, as long as the confined exciton is allowed to rotate around the opening of the anisotropic ring structure, which has a finite rim width.

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem DensityFunctional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy densityfunctionals that go beyond the GGA level must be employed

By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem DensityFunctional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn-Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn-Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy densityfunctionals that go beyond the GGA level must be employed.

Deriving accurate energy densityfunctional is one of the central problems in condensed matter physics, nuclear physics, and quantum chemistry. We propose a novel method to deduce the energy densityfunctional by combining the idea of the functional renormalization group and the Kohn-Sham scheme in densityfunctional theory. The key idea is to solve the renormalization group flow for the effective action decomposed into the mean-field part and the correlation part. Also, we propose a simple practical method to quantify the uncertainty associated with the truncation of the correlation part. By taking the φ4 theory in zero dimension as a benchmark, we demonstrate that our method shows extremely fast convergence to the exact result even for the highly strong coupling regime.

Densityfunctional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to

Densityfunctional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to iteratively construct

Estimation of quantum states is an important step in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not positive, and hence not physically acceptable. How do we ensure that at all stages of reconstruction, we keep the density matrix positive? Recently a method has been suggested based on maximum likelihood estimation, wherein the density matrix is guaranteed to be positive definite. We experimentally implement this protocol on an NMR quantum information processor. We discuss several examples and compare with the standard method of state estimation. - Highlights: • State estimation using maximum likelihood method was performed on an NMR quantum information processor. • Physically valid density matrices were obtained every time in contrast to standard quantum state tomography. • Density matrices of several different entangled and separable states were reconstructed for two and three qubits.

We discuss the source of errors in semiempirical densityfunctional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham densityfunctional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

Full text: Because of the negative mass dimension of the coupling constant perturbative Einstein quantum gravity (EQG) is nonrenormalizable. However, one can still make sense of EQG if it's interpreted as an effective field theory within a low energy expansion of a more fundamental theory. In an effective field theory all interactions compatible with its essential symmetry content are in principle allowed into the Lagrangian and thus it establishes a systematic framework to calculate quantum gravitational effects. This approach has been used to study the asymptotic behavior at high energies of quantum field theories that incorporate the gravitational field. Some studies analyze the asymptotic freedom for the coupling constants of some theories including gravitation near the Planck scale. For example, Robinson and Wilczek suggest that the gravitational field improve the asymptotic freedom of pure Yang-Mills near the Planck scale. Already , a similar calculation in the Maxwell-Einstein theory suggest that such conclusion is gauge dependence. This result was obtained by Pietrykowski. D. Toms say what the effective action is calculated in a gauge-condition independent version of the background field method using dimensional regularization it's argued that the gravitational field plays no role in the beta function of the Yang-Mills coupling. Another calculation done by Ebert, Plefka and Rodigast using conventional diagrammatic methods confirms the result obtained by Toms. In a recent publication, again published by Toms in 2010, claimed that quadratic divergent contributions were responsible to improve asymptotic freedom of fine structure constant by quantum gravity effects by using proper time cutoff regularization and effective action methods. However, the physical reality of the result in Tom's was questioned in recent work. This purpose of this work is to shed light on the origin of such controversies using only a diagrammatic analysis. As an effective model EQG is

Most colloids usually exhibit one or several polydispersities. A natural framework for the theoretical description of polydisperse systems is provided by the extension of densityfunctional theory to 'continuous' mixtures. This will be illustrated here by the study of both the bulk and interfacial properties of a simple van der Waals model for a polydisperse colloidal fluid. (author)

Densityfunctional theory (DFT) calculations have been carried out for hydrated L-alanine, L-alanyl-L-alanine and N-acetyl L-alanine N'-methylamide and examined with respect to the effect of water on the structure, the vibrational frequencies, vibrational absorption (VA) and vibrational circular...

In his review, D. Scalapino identified two serious limitations on the application of Quantum Monte Carlo (QMC) methods to the models of interest in High T c Superconductivity (HTS). One is the ''sign problem''. The other is the ''analytic continuation problem'', which is how to extract electron spectral functions from QMC calculations of the imaginary time Green's functions. Through-out this Symposium on HTS, the spectral functions have been the focus for the discussion of normal state properties including the applicability of band theory, Fermi liquid theory, marginal Fermi liquids, and novel non-perturbative states. 5 refs., 1 fig

Highlights: • In contrast to a s-wave superconductor, the quantum correlation of the d-wave superconductor is sensitive to the change of the gap magnitude. • Quantum discord of the d-wave superconductor oscillates. • Quantum discord becomes zero at a characteristic length of the d-wave superconductor. • Quantum correlation strongly depends on the length of grain. Length of the superconductor lower, the quantum correlation length higher. • Quantum tripartite entanglement for a nano-scale d-wave superconductor is better than for a bulk d-wave superconductor. - Abstract: By approximating the energy gap, entering nano-size effect via gap fluctuation and calculating the Green's functions and the space-spin density matrix, the dependence of quantum correlation (entanglement, discord and tripartite entanglement) on the relative distance of two electron spins forming Cooper pairs, the energy gap and the length of bulk and nano interacting Fermi system (a nodal d-wave superconductor) is determined. In contrast to a s-wave superconductor, quantum correlation of the system is sensitive to the change of the gap magnitude and strongly depends on the length of the grain. Also, quantum discord oscillates. Furthermore, the entanglement length and the correlation length are investigated. Discord becomes zero at a characteristic length of the d-wave superconductor.

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

After briefly reviewing the definitions of classical probability densities for position, P C L(x), and for momentum, P C L(p), we present several examples of classical mechanical potential systems, mostly variations on such familiar cases as the infinite well and the uniformly accelerated particle for which the classical distributions can be easily derived and visualized. We focus especially on a simple potential which interpolates between the symmetric linear potential, V(x)=F vertical bar x vertical bar, and the infinite well, which can illustrate, in a mathematically straightforward way, how the divergent δ-function classical probability density for momentum for the infinite well can be seen to arise. Such examples can help students understand the quantum mechanical momentum-space wavefunction (and its corresponding probability density) in much the same way that other semiclassical techniques, such as the WKB approximation, can be used to visualize position-space wavefunctions. (author)

This talk describes a new project in SciDAC II in the area of low-energy nuclear physics. The motivation and goals of the SciDAC are presented as well as an outline of the theoretical and computational methodology that will be employed. An important motivation is to have more accurate and reliable predictions of nuclear properties including their binding energies and low-energy reaction rates. The theoretical basis is provided by densityfunctional theory, which the only available theory that can be systematically applied to all nuclei. However, other methodologies based on wave function methods are needed to refine the functionals and to make applications to dynamic processes

An efficient densityfunctional algorithm (DFA) that scales linearly with system size will revolutionize electronic structure calculations. Densityfunctional calculations are reliable and accurate in determining many condensed matter and molecular ground-state properties. However, because current DFA's, including methods related to that of Car and Parrinello, scale with the cube of the system size, densityfunctional studies are not routinely applied to large systems. Linear scaling is achieved by constructing functions that are both localized and fully occupied, thereby eliminating the need to calculate global eigenfunctions. It is, however, widely believed that exponential localization requires the existence of an energy gap between the occupied and unoccupied states. Despite this, the authors demonstrate that linear scaling can still be achieved for metals. Using a linear scaling algorithm, they have explicitly constructed localized, almost fully occupied orbitals for the quintessential metallic system, jellium. The algorithm is readily generalizable to any system geometry and Hamiltonian. They will discuss the conceptual issues involved, convergence properties and scaling for their new algorithm

Pseudocolor processing is a branch of image enhancement. It dyes grayscale images to color images to make the images more beautiful or to highlight some parts on the images. This paper proposes a quantum image pseudocolor coding scheme based on the density-stratified method which defines a colormap and changes the density value from gray to color parallel according to the colormap. Firstly, two data structures: quantum image GQIR and quantum colormap QCR are reviewed or proposed. Then, the quantumdensity-stratified algorithm is presented. Based on them, the quantum realization in the form of circuits is given. The main advantages of the quantum version for pseudocolor processing over the classical approach are that it needs less memory and can speed up the computation. Two kinds of examples help us to describe the scheme further. Finally, the future work are analyzed.

Demonstrates how anyone in math, science, and engineering can master DFT calculations Densityfunctional theory (DFT) is one of the most frequently used computational tools for studying and predicting the properties of isolated molecules, bulk solids, and material interfaces, including surfaces. Although the theoretical underpinnings of DFT are quite complicated, this book demonstrates that the basic concepts underlying the calculations are simple enough to be understood by anyone with a background in chemistry, physics, engineering, or mathematics. The authors show how the widespread availability of powerful DFT codes makes it possible for students and researchers to apply this important computational technique to a broad range of fundamental and applied problems. DensityFunctional Theory: A Practical Introduction offers a concise, easy-to-follow introduction to the key concepts and practical applications of DFT, focusing on plane-wave DFT. The authors have many years of experience introducing DFT to studen...

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal densityfunctional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal densityfunctional for fermions. At the same time, statements of the densityfunctional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.

This manuscript presents the second, consistent densityfunctional in the QTP (Quantum Theory Project) family, that is, the CAM-QTP(01). It is a new range-separated exchange-correlation functional in which the non-local exchange contribution is 100% at large separation. It follows the same basic principles of this family that the Kohn-Sham eigenvalues of the occupied orbitals approximately equal the vertical ionization energies, which is not fulfilled by most of the traditional densityfunctional methods. This new CAM-QTP(01) functional significantly improves the accuracy of the vertical excitation energies especially for the Rydberg states in the test set. It also reproduces many other properties such as geometries, reaction barrier heights, and atomization energies.

Ferrogels consist of magnetic colloidal particles embedded in an elastic polymer matrix. As a consequence, their structural and rheological properties are governed by a competition between magnetic particle-particle interactions and mechanical matrix elasticity. Typically, the particles are permanently fixed within the matrix, which makes them distinguishable by their positions. Over time, particle neighbors do not change due to the fixation by the matrix. Here we present a classical densityfunctional approach for such ferrogels. We map the elastic matrix-induced interactions between neighboring colloidal particles distinguishable by their positions onto effective pairwise interactions between indistinguishable particles similar to a ‘pairwise pseudopotential’. Using Monte-Carlo computer simulations, we demonstrate for one-dimensional dipole-spring models of ferrogels that this mapping is justified. We then use the pseudopotential as an input into classical densityfunctional theory of inhomogeneous fluids and predict the bulk elastic modulus of the ferrogel under various conditions. In addition, we propose the use of an ‘external pseudopotential’ when one switches from the viewpoint of a one-dimensional dipole-spring object to a one-dimensional chain embedded in an infinitely extended bulk matrix. Our mapping approach paves the way to describe various inhomogeneous situations of ferrogels using classical densityfunctional concepts of inhomogeneous fluids.

This book contains a systematic presentation of quantumfunctional analysis, a mathematical subject also known as operator space theory. Created in the 1980s, it nowadays is one of the most prominent areas of functional analysis, both as a field of active research and as a source of numerous important applications. The approach taken in this book differs significantly from the standard approach used in studying operator space theory. Instead of viewing "quantized coefficients" as matrices in a fixed basis, in this book they are interpreted as finite rank operators in a fixed Hilbert space. This allows the author to replace matrix computations with algebraic techniques of module theory and tensor products, thus achieving a more invariant approach to the subject. The book can be used by graduate students and research mathematicians interested in functional analysis and related areas of mathematics and mathematical physics. Prerequisites include standard courses in abstract algebra and functional analysis.

It is shown that the exchange-correlation functional of spin-densityfunctional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-densityfunctional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-densityfunctional and a nonlocal current-densityfunctional. copyright 1997 The American Physical Society

We propose a new formulation of the correlation energy functional derived from the transcorrelated method in use in densityfunctional theory (TC-DFT). An effective Hamiltonian, H TC , is introduced by a similarity transformation of a many-body Hamiltonian, H, with respect to a complex function F: H TC =1FHF. It is proved that an expectation value of H TC for a normalized single Slater determinant, D n , corresponds to the total energy: E[n] = ⟨Ψ n |H|Ψ n ⟩/⟨Ψ n |Ψ n ⟩ = ⟨D n |H TC |D n ⟩ under the two assumptions: (1) The electron density nr associated with a trial wave function Ψ n = D n F is v-representable and (2) Ψ n and D n give rise to the same electron density nr. This formulation, therefore, provides an alternative expression of the total energy that is useful for the development of novel correlation energy functionals. By substituting a specific function for F, we successfully derived a model correlation energy functional, which resembles the functional form of the screened exchange method. The proposed functional, named the extended screened exchange (ESX) functional, is described within two-body integrals and is parametrized for a numerically exact correlation energy of the homogeneous electron gas. The ESX functional does not contain any ingredients of (semi-)local functionals and thus is totally free from self-interactions. The computational cost for solving the self-consistent-field equation is comparable to that of the Hartree-Fock method. We apply the ESX functional to electronic structure calculations for a solid silicon, H - ion, and small atoms. The results demonstrate that the TC-DFT formulation is promising for the systematic improvement of the correlation energy functional.

In little more than 20 years, the number of applications of the densityfunctional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of densityfunctional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why—50 years after its modern formulation and after two decades of rapid expansion—some of the most cited practitioners in the field are concerned about its future are discussed.

Proofs from different theoretical frameworks, namely, the Hohenbergh-Kohn theorems, the Kohn-Sham scheme, and the first-order density matrix representation, have been presented in this paper to show that the functional derivative of the noninteracting kinetic energy densityfunctional can uniquely be expressed as the negative of the Kohn-Sham effective potential, arbitrary only to an additive orbital-independent constant. Key points leading to the current result as well as confusion about the quantity in the literature are briefly discussed

Full Text Available We first propose two types of concepts of almost automorphic functions on the quantum time scale. Secondly, we study some basic properties of almost automorphic functions on the quantum time scale. Then, we introduce a transformation between functions defined on the quantum time scale and functions defined on the set of generalized integer numbers; by using this transformation we give equivalent definitions of almost automorphic functions on the quantum time scale; following the idea of the transformation, we also give a concept of almost automorphic functions on more general time scales that can unify the concepts of almost automorphic functions on almost periodic time scales and on the quantum time scale. Finally, as an application of our results, we establish the existence of almost automorphic solutions of linear and semilinear dynamic equations on the quantum time scale.

Densityfunctional theory calculations using Becke's three-parameter exchange functional in combination with the Lee-Young-Parr correlation functional (B3-LYP) and standard 6-311 + G(d,p) basis set were carried out to study the conformational stability and vibrational spectra of gamma-aminopropyltriethoxysilane. Calculations reveal the existence of two stable conformers trans and gauche. The calculated energy for the gauche conformation was found to be 608 cm -1 above the minimum energy of the trans conformation. Temperature dependence of Raman spectra of liquid APTES and DFT calculation enabled us to identify the vibrational bands characteristic for both conformers. It has been shown that there is an increase in the population of gauche conformer with increasing temperature

A polymer densityfunctional theory (P-DFT) has been extended to the case of quantum statistics within the framework of Feynman path integrals. We start with the exact P-DFT formalism for an ideal open chain and adapt its efficient numerical solution to the case of a ring. We show that, similarly......, the path integral problem can, in principle, be solved exactly by making use of the two-particle pair correlation function (2p-PCF) for the ends of an open polymer, half of the original. This way the exact data for one-dimensional quantum harmonic oscillator are reproduced in a wide range of temperatures....... The exact solution is not, though, reachable in three dimensions (3D) because of a vast amount of storage required for 2p-PCF. In order to treat closed paths in 3D, we introduce a so-called "open ring" approximation which proves to be rather accurate in the limit of long chains. We also employ a simple self...

Within the frame of the recently introduced phase space representation of non relativistic quantum mechanics, we propose a Lagrangian from which the phase space Schrodinger equation can be derived. From that Lagrangian, the associated conservation equations, according to Noether's theorem, are obtained. This shows that one can analyze quantum systems completely in phase space as it is done in coordinate space, without additional complications.

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the ''telegraphic'' approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close - if not identical - to the full answer in the strong sign-problem regime. (orig.)

A two-dimensional electron liquid (TDEL), subjected to a smooth random potential, is studied in the regime of the fractional quantum Hall effect. An analytical theory of the nonlinear screening is presented for the case when the fractional gap is much less than the magnitude of the unscreened random potential. In this ``narrow-gap approximation'' (NGA), we calculate the electron density distribution function, the fraction of the TDEL which is in the incompressible state, and the thermodynamic density of states. The magnetocapacitance is calculated to compare with the recent experiments. The NGA is found to be not accurate enough to describe the data. The results for larger fractional gaps are obtained by computer modeling. To fit the recent experimental data we have also taken into account the anyon-anyon interaction in the vicinity of a fractional singularity.

Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analog. The smallness arises from an almost uniform distribution for the phase of the fermion determinant. Large cancellations upon integration is the origin of a poor signal to noise ratio. We study three alternatives for this integration: the Gaussian approximation, the "telegraphic" approximation, and a novel expansion in terms of theory-dependent moments and universal coefficients. We have tested the methods for QCD at finite densities of heavy quarks. We find that for two of the approximations the results are extremely close—if not identical—to the full answer in the strong sign-problem regime.

We investigate the use of growth interruption to obtain low-density InAs quantum dots (QDs) on GaAs. The process was realized by Ostwald-type ripening of a thin InAs layer. It was found that the optical properties of the QDs as a function of growth interruption strongly depend on InAs growth rate. By using this approach, a low density of QDs (4 dots/μm 2 ) with uniform size distribution was achieved. As compared to QDs grown without growth interruption, a larger energy separation between the QD confined levels was observed, suggesting a situation closer to the ideal zero-dimensional system. Combining with an InGaAs capping layer such as In-rich QDs enable 1.3 μm emission at 4 K

Densityfunctional theory for superconductors (SCDFT) is a fully parameter-free approach to superconductivity that allows for accurate predictions of critical temperature and properties of superconductors. We report on the most recent extensions of the method, in particular the development of new functionals to: (1) incorporate in a correct fashion Migdal's theorem; (2) compute the excitation spectrum; (3) include spin-fluctuation mediated pairing Applications and predictions are shown for a set of materials, including conventional and unconventional superconductors.

A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability densityfunctions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.

to a specific number of eigenchannels. The transitions between plateaus can be abrupt in connection with structural rearrangements or extend over a few a of elongation. The interplay between conductance modes and structural deformation is discussed by means of the eigenchannel transmission probabilities.......We study the deformation and breaking of an atomic-sized sodium wire using densityfunctional simulations. The wire deforms through sudden atomic rearrangements and smoother atomic displacements. The conductance of the wire exhibits plateaus at integer values in units of 2e(2)/h corresponding...

In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated. (general)

Full text: Gibbons et al. have recently defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize the set C d of states having non-negative W simultaneously in all definitions of W in this class. I then argue that states in this set behave classically in a well-defined computational sense. I show that one-qubit states in C 2 do not provide for universal computation in a recent model proposed by Bravyi and Kitaev [quant-ph/0403025]. More generally, I show that the only pure states in C d are stabilizer states, which have an efficient description using the stabilizer formalism. This result shows that two different notions of 'classical' states coincide: states with non-negative Wigner functions are those which have an efficient description. This suggests that negativity of W may be necessary for exponential speed-up in pure-state quantum computation. (author)

Simulations in the warm dense matter regime using finite temperature Kohn-Sham densityfunctional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy KS eigenstates which are obtained from subspace diagonalization. We have developed a stochastic method for applying FT-KS-DFT, that overcomes the bottleneck of calculating the occupied KS orbitals by directly obtaining the density from the KS Hamiltonian. The proposed algorithm scales as O (" close=")N3T3)">N T-1 and is compared with the high-temperature limit scaling O density approximation (LDA); we demonstrate its efficiency, statistical errors, and bias in the estimation of the free energy per electron for a diamond structure silicon. The bias is small compared to the fluctuations and is independent of system size. In addition to calculating the free energy itself, one can also use the method to calculate its derivatives and obtain the equations of state.

Full Text Available This letter reports on how the Wilson flow technique can efficaciously kill the short-distance quantum fluctuations of 2- and 3-gluon Green functions, remove the ΛQCD scale and destroy the transition from the confining non-perturbative to the asymptotically-free perturbative sector. After the Wilson flow, the behavior of the Green functions with momenta can be described in terms of the quasi-classical instanton background. The same behavior also occurs, before the Wilson flow, at low-momenta. This last result permits applications as, for instance, the detection of instanton phenomenological properties or a determination of the lattice spacing only from the gauge sector of the theory.

To address ultimate precision in densityfunctional theory calculations we employ the full-potential linearized augmented plane-wave + local-orbital (LAPW + lo) method and justify its usage as a benchmark method. LAPW + lo and two completely unrelated numerical approaches, the multiresolution analysis (MRA) and the linear combination of atomic orbitals, yield total energies of atoms with mean deviations of 0.9 and 0.2 μ Ha , respectively. Spectacular agreement with the MRA is reached also for total and atomization energies of the G2-1 set consisting of 55 molecules. With the example of α iron we demonstrate the capability of LAPW + lo to reach μ Ha /atom precision also for periodic systems, which allows also for the distinction between the numerical precision and the accuracy of a given functional.

forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators......Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional...... theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed...

The new edition of a standard reference will be of interest to advanced students wishing to become familiar with the method of Green's functions for obtaining simple and general solutions to basic problems in quantum physics. The main part is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and bound level information. The bound-level treatment gives a clear physical understanding of ''difficult'' questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book. This third edition is 50% longer than the previous and offers end-of-chapter problems and solutions (40% are solved) and additional appendices to help it is to serve as an effective self-tutorial and self-sufficient reference. Throughout, it demonstrates the powerful and unifying formalism of Green's functions across many applications, including transport properties, carbon nanotubes, and photonics and photonic crystals. (orig.)

This book is on quantal densityfunctional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2 nd edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn densityfunctional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

The filtered densityfunction (FDF) closure is extended to a “self-contained” format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass densityfunction (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. We demonstrated how LES is conducted of a turbulent shear flow with transport of a passive scalar. Finally, the consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

The filtered densityfunction (FDF) closure is extended to a "self-contained" format to include the subgrid-scale (SGS) statistics of all of the hydro-thermo-chemical variables in turbulent flows. These are the thermodynamic pressure, the specific internal energy, the velocity vector, and the composition field. In this format, the model is comprehensive and facilitates large-eddy simulation (LES) of flows at both low and high compressibility levels. A transport equation is developed for the joint pressure-energy-velocity-composition filtered mass densityfunction (PEVC-FMDF). In this equation, the effect of convection appears in closed form. The coupling of the hydrodynamics and thermochemistry is modeled via a set of stochastic differential equation for each of the transport variables. This yields a self-contained SGS closure. For demonstration, LES is conducted of a turbulent shear flow with transport of a passive scalar. The consistency of the PEVC-FMDF formulation is established, and its overall predictive capability is appraised via comparison with direct numerical simulation (DNS) data.

This book is on quantal densityfunctional theory (QDFT) which is a time-dependent local effective potential theory of the electronic structure of matter. The time-independent QDFT constitutes a special case. The 2{sup nd} edition describes the further development of the theory, and extends it to include the presence of an external magnetostatic field. The theory is based on the 'quantal Newtonian' second and first laws for the individual electron. These laws are in terms of 'classical' fields that pervade all space, and their quantal sources. The fields are separately representative of the electron correlations that must be accounted for in local potential theory. Recent developments show that irrespective of the type of external field the electrons are subject to, the only correlations beyond those due to the Pauli exclusion principle and Coulomb repulsion that need be considered are solely of the correlation-kinetic effects. Foundational to QDFT, the book describes Schroedinger theory from the new perspective of the single electron in terms of the 'quantal Newtonian' laws. Hohenberg-Kohn densityfunctional theory (DFT), new understandings of the theory and its extension to the presence of an external uniform magnetostatic field are described. The physical interpretation via QDFT, in terms of electron correlations, of Kohn-Sham DFT, approximations to it and Slater theory are provided.

There have been many significant advances in time-dependent densityfunctional theory over recent years, both in enlightening the fundamental theoretical basis of the theory, as well as in computational algorithms and applications. This book, as successor to the highly successful volume Time-Dependent DensityFunctional Theory (Lect. Notes Phys. 706, 2006) brings together for the first time all recent developments in a systematic and coherent way. First, a thorough pedagogical presentation of the fundamental theory is given, clarifying aspects of the original proofs and theorems, as well as presenting fresh developments that extend the theory into new realms such as alternative proofs of the original Runge-Gross theorem, open quantum systems, and dispersion forces to name but a few. Next, all of the basic concepts are introduced sequentially and building in complexity, eventually reaching the level of open problems of interest. Contemporary applications of the theory are discussed, from real-time coupled-electron-ion dynamics, to excited-state dynamics and molecular transport. Last but not least, the authors introduce and review recent advances in computational implementation, including massively parallel architectures and graphical processing units. Special care has been taken in editing this volume as a multi-author textbook, following a coherent line of thought, and making all the relevant connections between chapters and concepts consistent throughout. As such it will prove to be the text of reference in this field, both for beginners as well as expert researchers and lecturers teaching advanced quantum mechanical methods to model complex physical systems, from molecules to nanostructures, from biocomplexes to surfaces, solids and liquids. (orig.)

We describe the density profiles of confined atomic Bose gases in the high-rotation limit, in single-layer and multilayer geometries. We show that, in a local-density approximation, the density in a single layer shows a landscape of quantized steps due to the formation of incompressible liquids, which are analogous to fractional quantum Hall liquids for a two-dimensional electron gas in a strong magnetic field. In a multilayered setup we find different phases, depending on the strength of the interlayer tunneling t. We discuss the situation where a vortex lattice in the three-dimensional condensate (at large tunneling) undergoes quantum melting at a critical tunneling t c 1 . For tunneling well below t c 1 one expects weakly coupled or isolated layers, each exhibiting a landscape of quantum Hall liquids. After expansion, this gives a radial density distribution with characteristic features (cusps) that provide experimental signatures of the quantum Hall liquids

It is shown that the expressions for the free energy density of ideal quantum gases in the canonical and grand canonical ensembles, are identical up to additive terms which vanish in the thermodynamic limit. (orig.)

The quantum mechanical ground state of electrons is described by DensityFunctional Theory, which leads to large minimization problems. An efficient minimization method uses a self-consistent field (SCF) solution of large eigenvalue problems. The iterative Davidson algorithm is often used, and we...

Methods of finite temperature quantum field theory are used to construct the g-Hartree densityfunctional for atoms. Low and high temperature expansions are discussed in detail. Numerical studies for atomic ground-state configurations are presented in the Thomas-Fermi-Scaling limit. (orig.)

Recent work in the field of probability density estimation has included the introduction of some new methods, such as the polynomial and spline methods and the nearest neighbor method, and the study of asymptotic properties in depth. This earlier work is summarized here. In addition, the computational complexity of the various algorithms is analyzed, as are some simulations. The object is to compare the performance of the various methods in small samples and their sensitivity to change in their parameters, and to attempt to discover at what point a sample is so small that density estimation can no longer be worthwhile. (RWR)

It is shown that the functional derivatives in density-functional theory (DFT) can be explicitly defined within the domain of electron densities restricted by the electron number, and a constructive definition of such restricted derivatives is suggested. With this definition, Kohn-Sham (KS) equations can be established for an N-electron system without extending the functional domain and introducing a Lagrange multiplier. This may clarify some of the fundamental questions raised by Nesbet (1998 Phys. Rev. A 58 R12). The definition naturally leads to the fact that the KS effective potential is determined only to within an additive constant, thus the KS levels can shift freely and the relation between the highest occupied molecular orbital (HOMO) energy and the ionization potential of the system depends on the choice of the constant. On the other hand, if the domain of functionals is indeed extended beyond the electron number restriction, conclusions depend on whether the extended functionals have unrestricted derivatives or not. It is shown that the ensemble extension of DFT to open systems of mixed states (Perdew et al 1982 Phys. Rev. Lett. 49 1691) leads to an energy functional which has no unrestricted derivative at integer electron numbers. Hence after this extension, the relation between the HOMO energy and the ionization potential for an N-electron system is still uncertain. Besides, there are different extensions of the energy functional to a domain of densities unrestricted by the integer electron number, resulting in different unrestricted derivatives and electron systems with different chemical potentials. Even for the exact exchange-correlation potential, there is still an undetermined constant, whether it is a restricted or unrestricted derivative

A study of the photoluminescence from a four-period Cd x Hg 1-x Te multiple quantum well structure at 11 K as a function of excitation density is presented. High-resolution X-ray diffraction and transmission electron microscopy revealed that the quantum well structure is of high quality. This was supported by the narrow photoluminescence peak originating in the ground state electron - heavy hole transition, with a full width at half maximum of only 7.4 meV for an excitation density of 1.3 W/cm 2 . When the excitation density was increased from 1.3 to 23.4 W/cm 2 , the peak position was shifted toward higher energy by 2.6 meV and the full width at half maximum increased from 7.4 to 10.9 meV

The quantum mechanical treatment of both electrons and protons in the calculation of excited state properties is critical for describing nonadiabatic processes such as photoinduced proton-coupled electron transfer. Multicomponent densityfunctional theory enables the consistent quantum mechanical treatment of more than one type of particle and has been implemented previously for studying ground state molecular properties within the nuclear-electronic orbital (NEO) framework, where all electrons and specified protons are treated quantum mechanically. To enable the study of excited state molecular properties, herein the linear response multicomponent time-dependent densityfunctional theory (TDDFT) is derived and implemented within the NEO framework. Initial applications to FHF - and HCN illustrate that NEO-TDDFT provides accurate proton and electron excitation energies within a single calculation. As its computational cost is similar to that of conventional electronic TDDFT, the NEO-TDDFT approach is promising for diverse applications, particularly nonadiabatic proton transfer reactions, which may exhibit mixed electron-proton vibronic excitations.

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark-gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent

We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark-gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.

Three densityfunctional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe 2 O 3 , Fe 3 O 4 , and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.

We study the behaviour of the normal derivative of eigenfunctions of the Helmholtz equation inside billiards with Dirichlet boundary condition. These boundary functions are of particular importance because they uniquely determine the eigenfunctions inside the billiard and also other physical quantities of interest. Therefore, they form a reduced representation of the quantum system, analogous to the Poincare section of the classical system. For the normal derivatives we introduce an equivalent to the standard Green function and derive an integral equation on the boundary. Based on this integral equation we compute the first two terms of the mean asymptotic behaviour of the boundary functions for large energies. The first term is universal and independent of the shape of the billiard. The second one is proportional to the curvature of the boundary. The asymptotic behaviour is compared with numerical results for the stadium billiard, different limacon billiards and the circle billiard, and good agreement is found. Furthermore, we derive an asymptotic completeness relation for the boundary functions

Autoionizing states are inaccessible to time-dependent densityfunctional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.

The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.

The time behavior of a phase correlation function for dynamical quantum systems which are classically chaotic is considered. It is shown that under certain conditions there are three time regions of the quantum correlations behavior; the region of classical stochasticity (exponential decay of quantum correlations); the region of the correlations decay with a power law; the region of the constant level of the quantum correlations. The boundaries of these time regions are presented. The estimation of a remaining level of the quantum correlations is given. (orig.)

We present recent advances in densityfunctional theory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer-Büttiker(LB) + DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as the temperature increases. To overcome the limitations of LB + DFT, the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on one-to-one correspondence between the pair of basic variables, steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths, thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation. - Highlights: • We study the Wigner function for a quantum spinless relativistic particle. • We discuss the relativistic Wigner function introduced by Zavialov and Malokostov. • We introduce relativistic Wigner function based on the standard definition. • We find analytic expressions for relativistic Wigner functions.

During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy densityfunctional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.

Photovoltaic devices, electrochemical cells, catalysis processes, light emitting diodes, scanning tunneling microscopes, molecular electronics, and related devices have one thing in common: open quantum systems where energy and matter are not conserved. Traditionally quantum chemistry is confined to isolated and closed systems, while quantum dissipation theory studies open quantum systems. The key quantity in quantum dissipation theory is the reduced system density matrix. As the reduced system density matrix is an O(M! × M!) matrix, where M is the number of the particles of the system of interest, quantum dissipation theory can only be employed to simulate systems of a few particles or degrees of freedom. It is thus important to combine quantum chemistry and quantum dissipation theory so that realistic open quantum systems can be simulated from first-principles. We have developed a first-principles method to simulate the dynamics of open electronic systems, the time-dependent densityfunctional theory for open systems (TDDFT-OS). Instead of the reduced system density matrix, the key quantity is the reduced single-electron density matrix, which is an N × N matrix where N is the number of the atomic bases of the system of interest. As the dimension of the key quantity is drastically reduced, the TDDFT-OS can thus be used to simulate the dynamics of realistic open electronic systems and efficient numerical algorithms have been developed. As an application, we apply the method to study how quantum interference develops in a molecular transistor in time domain. We include electron-phonon interaction in our simulation and show that quantum interference in the given system is robust against nuclear vibration not only in the steady state but also in the transient dynamics. As another application, by combining TDDFT-OS with Ehrenfest dynamics, we study current-induced dissociation of water molecules under scanning tunneling microscopy and follow its time dependent

For the description of ground-state correlation phenomena an accurate mapping of many-body quantum mechanics onto four particles is developed. The energy for a quantum system with no more than two-particle interactions may be expressed in terms of a two-particle reduced density matrix (2-RDM), but variational optimization of the 2-RDM requires that it corresponds to an N-particle wave function. We derive N-representability conditions on the 2-RDM that guarantee the validity of the uncertainty relations for all operators with two-particle interactions. One of these conditions is shown to be necessary and sufficient to make the RDM solutions of the dispersion condition equivalent to those from the contracted Schrödinger equation (CSE) [Mazziotti, Phys. Rev. A 57, 4219 (1998)]. In general, the CSE is a stronger N-representability condition than the dispersion condition because the CSE implies the dispersion condition as well as additional N-representability constraints from the Hellmann-Feynman theorem. Energy minimization subject to the representability constraints is performed for a boson model with 10, 30, and 75 particles. Even when traditional wave-function methods fail at large perturbations, the present method yields correlation energies within 2%.

In this paper, we determine the spectrum and density of states of a graphene quantum dot in a normal quantizing magnetic field. To accomplish this, we employ the retarded Green function for a magnetized, infinite-sheet graphene layer to describe the dynamics of a tightly confined graphene quantum dot subject to Landau quantization. Considering a δ (2) (r) potential well that supports just one subband state in the well in the absence of a magnetic field, the effect of Landau quantization is to 'splinter' this single energy level into a proliferation of many Landau-quantized states within the well. Treating the graphene sheet and dot as a closed system subject to a fully Hermitian Hamiltonian (including boundary conditions), there is no indication of decay of the Landau-quantized graphene dot states into the quantized states of the host graphene sheet for 'tight' confinement by the δ (2) (r) potential well, notwithstanding extension of the dot Green function (and eigenfunctions) outside the δ (2) (r) potential well.

We propose a practical scheme for calculating the ground-state pair density (PD) by utilizing the correlated wave function. As the correlated wave function, we adopt a linear combination of the single Slater determinants that are constructed from the solutions of the initial scheme [Higuchi M and Higuchi K 2007 Physica B 387, 117]. The single-particle equation is derived by performing the variational principle within the set of PDs that are constructed from such correlated wave functions. Since the search region of the PD is substantially extended as compared with the initial scheme, it is expected that the present scheme can cover more correlation effects. The single-particle equation is practical, and may be easily applied to actual calculations.

The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

The recently proposed local-scaling density-functional theory provides us with a practical method for the direct variational determination of the electron densityfunction ρ(r). The structure of ''orbits,'' which ensures the one-to-one correspondence between the electron density ρ(r) and the N-electron wave function Ψ({r k }), is studied in detail. For the realization of the local-scaling density-functional calculations, procedures for intraorbit and interorbit optimizations of the electron densityfunction are proposed. These procedures are numerically illustrated for the helium atom in its ground state at the beyond-Hartree-Fock level

The expression for the density matrix describing particles of one sort (electrons or positrons) created by an external electromagnetic field from the vacuum is obtained. The explicit form of the density matrix is found for the case of constant and uniform electric field. Arguments are given for the presence of a connection between the thermal nature of the density matrix describing particles created by the gravitational field of a black hole and the equivalence principle. (author)

Full Text Available Cognitive decline and dementia due to Alzheimer’s disease have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34 to 87 years old (62.78±9.27, were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after three years. Blood samples were collected for apolipoprotein E (APOE genotyping and dual energy x-ray absorptiometry (DXA was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms.

Densityfunctional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.

Densityfunctional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.

Background: Energy densityfunctional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the densityfunctional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy densityfunctional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure

Periodic hybrid-exchange densityfunctional theory calculations are used to explore the first layer of water at model oxide surfaces, which is an important step for understanding the photocatalytic reactions involved in solar water splitting. By comparing the structure and properties of SnO2(110) and TiO2(110) surfaces in contact with water, the effects of structural and electronic differences on the water chemistry are examined. The dissociative adsorption mode at low coverage (1/7 ML) up to monolayer coverage (1 ML) on both SnO2 and TiO2(110) surfaces is analysed. To investigate further the intermolecular interactions between adjacent adsorbates, monolayer adsorption on each surface is explored in terms of binding energies and bond lengths. Analysis of the water adsorption geometry and energetics shows that the relative stability of water adsorption on SnO2(110) is governed largely by the strength of the chemisorption and hydrogen bonds at the surface of the adsorbate-substrate system. However on TiO2(110), a more complicated scenario of the first layer of water on its surface arises in which there is an interplay between chemisorption, hydrogen bonding and adsorbate-induced atomic displacements in the surface. Furthermore the projected density of states of each surface in contact with a mixture of adsorbed water molecules and adsorbed hydroxyls is presented and sheds some light on the nature of the crystalline chemical bonds as well as on why adsorbed water has often been reported to be unstable on rutile SnO2(110).

We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by densityfunctional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.

The results of a numerical study of high-intensity X-ray laser beam interaction with warm quantum plasma (WQP) are presented. By means of an upward ramp density profile combined with quantum factors specially the Fermi velocity, we have demonstrated significant relativistic self-focusing (RSF) of a Gaussian electromagnetic beam in the WQP where the Fermi temperature term in the dielectric function is important. For this purpose, we have considered the quantum hydrodynamics model that modifies refractive index of inhomogeneous WQPs with the inclusion of quantum correction through the quantum statistical and diffraction effects in the relativistic regime. Also, to better illustration of the physical difference between warm and cold quantum plasmas and their effect on the RSF, we have derived the envelope equation governing the spot size of X-ray laser beam in Q-plasmas. In addition to the upward ramp density profile, we have found that the quantum effects would be caused much higher oscillation and better focusing of X-ray laser beam in the WQP compared to that of cold quantum case. Our computational results reveal the importance of the use of electrons density profile and Fermi speed in enhancing self-focusing of laser beam

The longitudinal and transverse spectral functions for arbitrary conserved and non-conserved vector and axial vector currents of massive quarks are calculated to first order in α/sub s/ and exact analytical expressions are given. As an intermediate step the form factors to the same order in α/sub s/ are determined. A remarkably simple result for the combination of the spectral functions corresponding to the Weinberg's first sum rule is derived. It behaves asymptotically like α/sub s/s 2 thus ensuring the convergence of the sum rule. The Weinberg's second sum rule is shown to fail to hold, a new sum rule is then proposed to replace the original one. The current algebra calculation of the pion electromagnetic mass difference is reexamined in the light of quantum chromodynamics. The old analysis cannot be upheld because of the failure of the Weinberg's second sum rule. After a modification based on Dashen's theorem, the proposed sum rule then can be used to obtain a mass difference close to experimental value. Using the derived QCD corrected spectral functions on finite Q 2 sum rules, the current couplings of the five low-lying mesons π, rho, K, K*, A 1 are computed. For values of quark masses m/sub u/ = m/sub d/ = 0.25 GeV, m/sub s/ = 0.4 GeV and of the QCD scale parameter Λ = 0.5 GeV, a striking agreement with experiment is obtained. We investigate decay properties of the intermediate vector bosons Z, W. Gluonic corrections to hadronic decay modes are calculated with the account of quark mass effect. Implications of the results for decay widths, branching ratios are examined. The ratio R of reaction e + e - → hadrons is calculated to first order in α/sub s/, the quark mass effect is shown to be important

We study the efficiency of quantum algorithms which aim at obtaining phase-space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions, and compared with the classical computation. Different procedures to extract more efficiently information from the final wave function of these algorithms are studied, including coarse-grained measurements, amplitude amplification, and measure of wavelet-transformed wave function. The algorithms are analyzed and numerically tested on a complex quantum system showing different behavior depending on parameters: namely, the kicked rotator. The results for the Wigner function show in particular that the use of the quantum wavelet transform gives a polynomial gain over classical computation. For the Husimi distribution, the gain is much larger than for the Wigner function and is larger with the help of amplitude amplification and wavelet transforms. We discuss the generalization of these results to the simulation of other quantum systems. We also apply the same set of techniques to the analysis of real images. The results show that the use of the quantum wavelet transform allows one to lower dramatically the number of measurements needed, but at the cost of a large loss of information.

In statistical mechanics, for a system with a fixed number of particles, e.g. a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the canonical partition function is difficult. In this paper, based on the mathematical theory of the symmetric function, we suggest a method for the calculation of the canonical partition function of ideal quantum gases, including ideal Bose, Fermi, and Gentile gases. Moreover, we express the canonical partition functions of interacting classical and quantum gases given by the classical and quantum cluster expansion methods in terms of the Bell polynomial in mathematics. The virial coefficients of ideal Bose, Fermi, and Gentile gases are calculated from the exact canonical partition function. The virial coefficients of interacting classical and quantum gases are calculated from the canonical partition function by using the expansion of the Bell polynomial, rather than calculated from the grand canonical potential.

Quasi-cyclic LDPC codes can approach the Shannon capacity and have efficient decoders. Manabu Hagiwara et al., 2007 presented a method to calculate parity check matrices with high girth. Two distinct, orthogonal matrices Hc and Hd are used. Using submatrices obtained from Hc and Hd by deleting rows, we can alter the code rate. The submatrix of Hc is used to correct Pauli X errors, and the submatrix of Hd to correct Pauli Z errors. We simulated this system for depolarizing noise on USC's High Performance Computing Cluster, and obtained the block error rate (BER) as a function of the error weight and code rate. From the rates of uncorrectable errors under different error weights we can extrapolate the BER to any small error probability. Our results show that this code family can perform reasonably well even at high code rates, thus considerably reducing the overhead compared to concatenated and surface codes. This makes these codes promising as storage blocks in fault-tolerant quantum computation. Error Correction using Quantum Quasi-Cyclic Low-Density Parity-Check(LDPC) Codes.

A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant energy condition. In a quantum field theory, there instead exists a quantum energy condition, i.e., a lower bound on the energy density that depends on information-theoretic quantities. Some extensions to higher dimensions are briefly discussed.

One of the vital ingredients in the theoretical tools useful in materials modeling at all the length scales of interest is the concept of density. In the microscopic length scale, it is the electron density that has played a major role in providing a deeper understanding of chemical binding in atoms, molecules and solids.

We analyze the electronic states in a cylindrical quantum well-wire (QWW) with randomly distributed neutral, D^0 and negatively charged D^- donors. In order to calculate the ground state energies of the off-center donors D^0 and D^- as a function of the distance from the axis of the QWW, we use the recently developed fractal dimension method [1]. There the problems are reduced to those similar for a hydrogen-like atom and a negative-hydrogen-like ion respectively, in an isotropic effective space with variable fractional dimension. The numerical trigonometric sweep method [2] and the three-parameter Hylleraas-type trial function are used to solve these problems. Novel curves for the density of impurity states in cylindrical QWWs with square-well, parabolic and soft-edge barrier potentials are present. Additionally we analyze the effect of the repulsive core on the density of the impurity states. [1] I.D. Mikhailov, F. J. Betancur, R. Escorcia and J. Sierra-Ortega, Phys. Stat. Sol., 234(b), 590 (2002) [2] F. J. Betancur, I. D. Mikhailov and L. E. Oliveira, J. Appl. Phys. D, 31, 3391(1998)

An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...... function. The relationship to the recent results by Torres-Vega and Frederick [J. Chem. Phys. 98, 3103 (1993)] is also discussed....

We perform a semiclassical expansion in the Wheeler-DeWitt equation, in powers of the gravitational constant. We then show that quantum gravitational fluctuations can provide a correction to the wave-functions which are solutions of the Schroedinger equation for matter. This also implies a correction to the expectation values of quantum mechanical observables. (author). 6 refs

I propose encoder and decoder architectures for entanglement-assisted (EA) quantum low-density parity-check (LDPC) codes suitable for all-optical implementation. I show that two basic gates needed for EA quantum error correction, namely, controlled-NOT (CNOT) and Hadamard gates can be implemented based on Mach-Zehnder interferometer. In addition, I show that EA quantum LDPC codes from balanced incomplete block designs of unitary index require only one entanglement qubit to be shared between source and destination.

We use densityfunctional theory (DFT) with a recently developed van der Waals densityfunctional (vdW-DF) to study the adsorption of graphene on Co, Ni, Pd, Ag, Au, Cu, Pt, and Al(111) surfaces. In contrast to the local-density approximation (LDA) which predicts relatively strong binding for Ni...

We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out around the partition function of the classical component of the Hamiltonian with the expansion parameter being the strength of the off-diagonal, or quantum, portion. To demonstrate the usefulness of the technique we analytically compute to third order the partition functions of the 1D Ising model with longitudinal and transverse fields, and the quantum 1D Heisenberg model.

The geometrical structure of any aggregate of atoms is one of its basic properties and, in principle, straightforward to predict. One chooses a structure, determines the total energy E of the system of electrons and ions, and repeats the calculation for all possible geometries. The ground state structure is that with the lowest energy. A quantum mechanical calculation of the exact wave function Ψ would lead to the total energy, but this is practicable only in very small molecules. Furthermore, the number of local minima in the energy surface increases dramatically with increasing molecular size. While traditional ab initio methods have had many impressive successes, the difficulties have meant that they have focused on systems with relatively few local minima, or have used experiments or experience to limit the range of geometries studied. On the other hand, calculations for much larger molecules and extended systems are often forced to use simplifying assumptions about the interatomic forces that limit their predictive capability. The approach described here avoids both of these extremes: Total energies of predictive value are calculated without using semi-empirical force laws, and the problem of multiple minima in the energy surface is addressed. The densityfunctional formalism, with a local density approximation for the exchange-correlation energy, allows one to calculate the total energy for a given geometry in an efficient, if approximate, manner. Calculations for heavier elements are not significantly more difficult than for those in the first row and provide an ideal way to study bonding trends. When coupled with finite-temperature molecular dynamics, this formalism can avoid many of the energetically unfavorable minima in the energy surface. We show here that the method leads to surprising and exciting results. (orig.)

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.

Modern techniques from quantum field theory are applied in this work to the description of ultracold quantum gases. This leads to a unified description of many phenomena including superfluidity for bosons and fermions, classical and quantum phase transitions, different dimensions, thermodynamic properties and few-body phenomena as bound state formation or the Efimov effect. The non-perturbative treatment with renormalization group flow equations can account for all known limiting cases by solving one single equation. It improves previous results quantitatively and brings qualitatively new insights. As an example, new quantum phase transitions are found for fermions with three spin states. Ultracold atomic gases can be seen as an interesting model for features of high energy physics and for condensed matter theory. The research reported in this thesis helps to solve the difficult complexity problem in modern theoretical physics. (orig.)

Exact schemes for the embedding of densityfunctional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid densityfunctional is employed.

Exact schemes for the embedding of densityfunctional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid densityfunctional is employed.

Exact schemes for the embedding of densityfunctional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid densityfunctional is employed.

Approximate kinetic energy densityfunctionals (KEDFs) are central to orbital-free densityfunctional theory. Limitations on the spatial derivative dependencies of KEDFs have been claimed from differential virial theorems. We identify a central defect in the argument: the relationships are not true for an arbitrary density but hold only for the minimizing density and corresponding chemical potential. Contrary to the claims therefore, the relationships are not constraints and provide no independent information about the spatial derivative dependencies of approximate KEDFs. A simple argument also shows that validity for arbitrary v-representable densities is not restored by appeal to the density-potential bijection.

The primary goal of Kohn-Sham densityfunctional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a densityfunctional can be affected by the electron density. Here we apply the nonempirical Tao-Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew-Burke-Ernzerhof (PBE), Tao-Perdew-Staroverov-Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree-Fock density yields the exchange and correlation energies in good agreement with the Optimized Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Finally, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.

In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent densityfunctional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f xc from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the propagation

In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent densityfunctional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f{sub xc} from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

We investigate the dynamics of water splitting on dye-sensitized metal (Ti, Cu) oxide surfaces, induced by direct sunlight excitation. In this study, we will consider the typical photoexcitation-followed-by-injection scheme, treating electron-injection and water splitting dynamics as independent events. The simultaneous modeling of the molecular motion and the quantum nonadiabatic transitions is achieved via the computation of the low-lying electronic states along several alternative reaction paths. Electronic structure calculations are based on a B3LYP-DFT Hamiltonian. The proposed approach combines an atomistic description of the reactants and of the immediate region of the surface, while the vibrational dynamics of the substrate is modeled as an effective bath leading to dissipation effects. The use of density-functional theory to solve the many- body electronic problem allows investigating the atomic motion of the water molecules and of a representative part of the substrate, thereby providing a theoretical and computational model capable to account simultaneously for the molecular character of the dye molecule and for the bulk properties of the surface. Furthermore, the insight emerging from this fundamental modeling can be used to optimize the chemical composition of the system to attain high incident-photon-flux-to-hydrogen-yield ratios. (full text)

Charge density determination from X-ray measurements necessitates the evaluation of the Fourier-Bessel transforms of the radial functions used to expand the charge density. Analytical expressions are given here for four sets of orthogonal functions which can substitute for the 'traditional exponential functions' set in least-squares refinements. (orig.)

We use the exact strong-interaction limit of the Hohenberg-Kohn energy densityfunctional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal densityfunctional whose functional derivative can be easily constructed,

An excitation dynamics of new quantum systems of N equidistant energy levels in a monochromatic field has been investigated. To obtain exact analytical solutions of dynamic equations an analytical method based on orthogonal functions of a real argument has been proposed. Using the orthogonal Legendre functions we have found an exact analytical expression for a population probability amplitude of the level n. Various initial conditions for the excitation of N-level quantum systems have been co...

It is shown that only the maximally entangled two-particle (spin 1/2) states whose one-particle reduced density matrix is p (i) = (1/2)I2 can realize the teleportation of an arbitrary one-particle spin state. Based on this,to teleport an arbitrary k-particle spin state, one must prepare an N-particle entangled state whose k-particle (k ＜ N) reduced density matrix has the structure 2-kI2k (I2k being the 2k × 2k identity matrix). The N-particle Greenberger-Horne-Zeilinger states cannot realize the teleportation of an arbitrary k-particle (N＞k≥2) state,except for special states with only two components.

Ensemble densityfunctional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble densityfunctional, E_{Hx}[n], in terms of the right derivative of the universal ensemble densityfunctional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.

Time-dependent (current) densityfunctional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows us to calculate the above basic variables by solving self-consistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems. In particular we show that it naturally leads to time-dependent densityfunctional theory for systems coupled to the Caldeira-Leggett bath.

This article develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error-correction performance, high rates, and low decoding complexity. The proposed method produces several infinite families of codes with a wide variety of parameters and entanglement requirements. Our framework encompasses the previously known entanglement-assisted quantum LDPC codes having the best error-correction performance and many other codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.

This book bridges the gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light. While suitable as a reference for the specialist in quantum optics, it also targets non-specialists from other disciplines who need to understand light and its uses in research. It introduces a single analytic tool, the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross-disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including optical tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency, squeezed light, and cavity quantum electrodynamics. A systematic approach starts with the simplest systems—stationary two-level atoms—then introduces atomic motion, adds more energy levels, and moves on to discuss first-, second-, and third-order coherence effects that are the basis for analyzing n...

The densityfunctional tight binding approach (DFTB) is well adapted for the study of point and line defects in graphene based systems. After briefly reviewing the use of DFTB in this area, we present a comparative study of defect structures, energies, and dynamics between DFTB results obtained using the dftb+ code, and densityfunctional results using the localized Gaussian orbital code, AIMPRO. DFTB accurately reproduces structures and energies for a range of point defect structures such as vacancies and Stone-Wales defects in graphene, as well as various unfunctionalized and hydroxylated graphene sheet edges. Migration barriers for the vacancy and Stone-Wales defect formation barriers are accurately reproduced using a nudged elastic band approach. Finally we explore the potential for dynamic defect simulations using DFTB, taking as an example electron irradiation damage in graphene. DFTB-MD derived sputtering energy threshold map for a carbon atom in a graphene plane. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

to fabricate high-density, pixelated (quarter video graphics array (QVGA) format), monochromatic and RGB quantum dots light-emitting diodes (QDLEDs), where inkjet printing is used to deposit the light-emitting layer of QDs. It shows some of the factors

This paper is about quantum heat defined as the change in energy of a bath during a process. The presentation takes into account recent developments in classical strong-coupling thermodynamics and addresses a version of quantum heat that satisfies quantum-classical correspondence. The characteristic function and the full counting statistics of quantum heat are shown to be formally similar. The paper further shows that the method can be extended to more than one bath, e.g., two baths at different temperatures, which opens up the prospect of studying correlations and heat flow. The paper extends earlier results on the expected quantum heat in the setting of one bath [E. Aurell and R. Eichhorn, New J. Phys. 17, 065007 (2015), 10.1088/1367-2630/17/6/065007; E. Aurell, Entropy 19, 595 (2017), 10.3390/e19110595].

We derive the basic formalism of densityfunctional theory for time-dependent electron-nuclear systems. The basic variables of this theory are the electron density in body-fixed frame coordinates and the diagonal of the nuclear N-body density matrix. The body-fixed frame transformation is carried

Local density approximation for the exchange energy is made for treatment of excited-states in density-functional theory. It is shown that taking care of the state-dependence of the LDA exchange energy functional leads to accurate excitation energies.

It is shown, for certain sequences [lambda/sub i/] in the complex plane, that linear combinations of the Breit-Wigner functions [B/sub i/] approximate, in the mean square, any function in L 2 (0,infinity). Implications and numerical use of this result are discussed

Full Text Available The relation of theWigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner–Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for directexperimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.

Quantum routers engineered with multiple frequency bands play a key role in quantum networks. We propose an experimentally accessible scheme for a multi-functionalquantum router, using photon-phonon conversion in a hybrid opto-electromechanical system. Our proposed device functions as a bidirectional, tunable multi-channel quantum router, and demonstrates the possibility to route single optical photons bidirectionally and simultaneously to three different output ports, by adjusting the microwave power. Further, the device also behaves as an interswitching unit for microwave and optical photons, yielding probabilistic routing of microwave (optical) signals to optical (microwave) outports. With respect to potential application, we verify the insignificant influence from vacuum and thermal noises in the performance of the router under cryogenic conditions.

Self-interaction error (SIE) is considered to be one of the major sources of error in most approximate exchange-correlation functionals for Kohn-Sham density-functional theory (KS-DFT), and it is large with all local exchange-correlation functionals and with some hybrid functionals. In this work, we consider systems conventionally considered to be dominated by SIE. For these systems, we demonstrate that by using multiconfiguration pair-densityfunctional theory (MC-PDFT), the error of a translated local density-functional approximation is significantly reduced (by a factor of 3) when using an MCSCF density and on-top density, as compared to using KS-DFT with the parent functional; the error in MC-PDFT with local on-top functionals is even lower than the error in some popular KS-DFT hybrid functionals. Density-functional theory, either in MC-PDFT form with local on-top functionals or in KS-DFT form with some functionals having 50% or more nonlocal exchange, has smaller errors for SIE-prone systems than does CASSCF, which has no SIE.

Plenty experimental evidence indicates that quantum critical phenomena give rise to much of the rich physics observed in strongly correlated itinerant electron systems such as the high temperature superconductors. A quantum critical point of particular interest is found at the zero-temperature onset of spin-density wave order in two-dimensional metals. The appropriate low-energy theory poses an exceptionally hard problem to analytic theory, therefore the unbiased and controlled numerical approach pursued in this thesis provides important contributions on the road to comprehensive understanding. After discussing the phenomenology of quantum criticality, a sign-problem-free determinantal quantum Monte Carlo approach is introduced and an extensive toolbox of numerical methods is described in a self-contained way. By the means of large-scale computer simulations we have solved a lattice realization of the universal effective theory of interest. The finite-temperature phase diagram, showing both a quasi-long-range spin-density wave ordered phase and a d-wave superconducting dome, is discussed in its entirety. Close to the quantum phase transition we find evidence for unusual scaling of the order parameter correlations and for non-Fermi liquid behavior at isolated hot spots on the Fermi surface.

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties of electronic systems. Here, we investigate an approach for the sampling of unbiased reduced density matrices within the full configuration interaction quantum Monte Carlo dynamic, which requires only small computational overheads. This is achieved via an independent replica population of walkers in the dynamic, sampled alongside the original population. The resulting reduced density matrices are free from systematic error (beyond those present via constraints on the dynamic itself) and can be used to compute a variety of expectation values and properties, with rapid convergence to an exact limit. A quasi-variational energy estimate derived from these density matrices is proposed as an accurate alternative to the projected estimator for multiconfigurational wavefunctions, while its variational property could potentially lend itself to accurate extrapolation approaches in larger systems

We show that the Wald Noether-charge entropy is canonically conjugate to the opening angle at the horizon. Using this canonical relation, we extend the Wheeler-DeWitt equation to a Schrödinger equation in the opening angle, following Carlip and Teitelboim. We solve the equation in the semiclassical approximation by using the correspondence principle and find that the solutions are minimal uncertainty wavefunctions with a continuous spectrum for the entropy and therefore also of the area of the black hole horizon. The fact that the opening angle fluctuates away from its classical value of 2π indicates that the quantum black hole is a superposition of horizonless states. The classical geometry with a horizon serves only to evaluate quantum expectation values in the strict classical limit.

The theory of discrete Wigner functions and of discrete quantum-state tomography [U. Leonhardt, Phys. Rev. Lett. 74, 4101 (1995)] is studied in more detail guided by the picture of precession tomography. Odd- and even-dimensional systems (angular momenta and spins, bosons, and fermions) are considered separately. Relations between simple number theory and the quantum mechanics of finite-dimensional systems are pointed out. In particular, the multicomplementarity of the precession states distinguishes prime dimensions from composite ones.

A density-functional theory is developed based on the Maxwell-Schrödinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current density-functional theory and an alternative to the paramagnetic current density-functional theory due to Vignale and Rasolt. The energy functional has strong enough convexity properties to allow a formulation that generalizes Lieb's convex analysis formulation of standard density-functional theory. Several variational principles as well as a Hohenberg-Kohn-like mapping between potentials and ground-state densities follow from the underlying convex structure. Moreover, the energy functional can be regarded as the result of a standard approximation technique (Moreau-Yosida regularization) applied to the conventional Schrödinger ground-state energy, which imposes limits on the maximum curvature of the energy (with respect to the magnetic field) and enables construction of a (Fréchet) differentiable universal densityfunctional.

Time-dependent densityfunctional theory (TD-DFT) is commonly used as the foundation to obtain neutral excited states and transition weights in DFT, but does not allow direct access to density of states and single-particle energies, i.e. ionisation energies and electron affinities. Here we show that by extending TD-DFT to a superfluid formulation, which involves operators that break particle-number symmetry, we can obtain the density of states and single-particle energies from the poles of an appropriate superfluid response function. The standard Kohn- Sham eigenvalues emerge as the adiabatic limit of the superfluid response under the assumption that the exchange- correlation functional has no dependence on the superfluid density. The Kohn- Sham eigenvalues can thus be interpreted as approximations to the ionisation energies and electron affinities. Beyond this approximation, the formalism provides an incentive for creating a new class of densityfunctionals specifically targeted at accurate single-particle eigenvalues and bandgaps.

This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

During the past several years, new types of geometric measure and dimension have been introduced; the packing measure and dimension, see [Su], [Tr] and [TT1]. These notions are playing an increasingly prevalent role in various aspects of dynamics and measure theory. Packing measure is a sort of dual of Hausdorff measure in that it is defined in terms of packings rather than coverings. However, in contrast to Hausdorff measure, the usual definition of packing measure requires two limiting procedures, first the construction of a premeasure and then a second standard limiting process to obtain the measure. This makes packing measure somewhat delicate to deal with. The question arises as to whether there is some simpler method for defining packing measure and dimension. In this paper, we find a basic limitation on this possibility. We do this by determining the descriptive set-theoretic complexity of the packing functions. Whereas the Hausdorff dimension function on the space of compact sets is Borel measurable, the packing dimension function is not. On the other hand, we show that the packing dimension functions are measurable with respect to the [sigma]-algebra generated by the analytic sets. Thus, the usual sorts of measurability properties used in connection with Hausdorff measure, for example measures of sections and projections, remain true for packing measure.

The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society

Full Text Available Propagation of a Gaussian x-ray laser beam has been analyzed in collisionless thermal quantum plasma with considering a ramped density profile. In this density profile due to the increase in the plasma density, an earlier and stronger self-focusing effect is noticed where the beam width oscillates with higher frequency and less amplitude. Moreover, the effect of the density profile slope and the initial plasma density on the laser propagation has been studied. It is found that, by increasing the initial density and the ramp slope, the laser beam focuses faster with less oscillation amplitude, smaller laser spot size and more oscillations. Furthermore, a comparison is made among the laser self-focusing in thermal quantum plasma, cold quantum plasma and classical plasma. It is realized that the laser self-focusing in the quantum plasma becomes stronger in comparison with the classical regime.

The employment of the numerical functional integration for the description of multidimensional systems in quantum and statistical physics is considered. For the multiple functional integrals with respect to Gaussian measures in the full separable metric spaces the new approximation formulas exact on a class of polynomial functionals of a given summary degree are constructed. The use of the formulas is demonstrated on example of computation of the Green function and the ground state energy in multidimensional Calogero model. 15 refs.; 2 tabs

Studying quantum turbulence the necessity of calculation the various characteristics of the vortex tangle (VT) appears. Some of 'crude' quantities can be expressed directly via the total length of vortex lines (per unit of volume) or the vortex line density L(t) and the structure parameters of the VT. Other more 'subtle' quantities require knowledge of the vortex line configurations {s(xi,t) }. Usually, the corresponding calculations are carried out with the use of more or less truthful speculations concerning arrangement of the VT. In this paper we review other way to solution of this problem. It is based on the trial distribution functional (TDF) in space of vortex loop configurations. The TDF is constructed on the basis of well established properties of the vortex tangle. It is designed to calculate various averages taken over stochastic vortex loop configurations. In this paper we also review several applications of the use this model to calculate some important characteristics of the vortex tangle. In particular we discussed the average superfluid mass current J induced by vortices and its dynamics. We also describe the diffusion-like processes in the nonuniform vortex tangle and propagation of turbulent fronts.

We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs

We investigate the construction of quantum low-density parity-check (LDPC) codes from classical quasicyclic (QC) LDPC codes with girth greater than or equal to 6. We have shown that the classical codes in the generalized Calderbank-Skor-Steane construction do not need to satisfy the dual-containing property as long as preshared entanglement is available to both sender and receiver. We can use this to avoid the many four cycles which typically arise in dual-containing LDPC codes. The advantage of such quantum codes comes from the use of efficient decoding algorithms such as sum-product algorithm (SPA). It is well known that in the SPA, cycles of length 4 make successive decoding iterations highly correlated and hence limit the decoding performance. We show the principle of constructing quantum QC-LDPC codes which require only small amounts of initial shared entanglement.

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian densityfunctional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent densityfunctional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. Furthermore, for systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can also be applied to a broad range of problems in materials science, chemistry, and biology

A computationally fast quantum mechanical molecular dynamics scheme using an extended Lagrangian densityfunctional tight-binding formulation has been developed and implemented in the DFTB+ electronic structure program package for simulations of solids and molecular systems. The scheme combines the computational speed of self-consistent densityfunctional tight-binding theory with the efficiency and long-term accuracy of extended Lagrangian Born-Oppenheimer molecular dynamics. For systems without self-consistent charge instabilities, only a single diagonalization or construction of the single-particle density matrix is required in each time step. The molecular dynamics simulation scheme can be applied to a broad range of problems in materials science, chemistry, and biology.

The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the arguments [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s 3 S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem

Using the effective mass approximation and variational method we have computed the effects of hydrostatic pressure on the absorption and photoluminescence spectra in spherical quantum dot GaAs-(Ga, Al) As, considering a finite confinement potential of this particular work we show the optical transitions in quantum of various sizes in the presence of hydrogenic impurities and hydrostatic pressure effects. Our first result describes the spectrum of optical absorption of 500 A QD for different values of hydrostatic pressure P = 0, 20 and 40 Kbar. The absorption peaks are sensitive to the displacement of the impurity center to the edge of the quantum dot and even more when the hydrostatic pressure changes in both cases showing that to the extent that these two effects are stronger quantum dots respond more efficiently. Also this result can be seen in the study of the photoluminescence spectrum as in the case of acceptor impurities consider them more efficiently capture carriers or electrons that pass from the conduction band to the valence band. Density states with randomly distributed impurity show that the additional peaks in the curves of the density of impurity states appear due to the presence of the additional hydrostatic pressure effects.

The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).

Full Text Available The properties of many materials at the atomic scale depend on the electronic structure, which requires a quantum mechanical treatment. The most widely used approach to make such a treatment feasible is densityfunctional theory (DFT, the advances in which were presented and discussed during the DFT conference in Debrecen. Some of these issues are presented in this Special Issue.

We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.

Full Text Available Identifying or constructing a fine-grained microscopic theory that will emerge under specific conditions to a known macroscopic theory is always a formidable challenge. Thermodynamics is perhaps one of the most powerful theories and best understood examples of emergence in physical sciences, which can be used for understanding the characteristics and mechanisms of emergent processes, both in terms of emergent structures and the emergent laws governing the effective or collective variables. Viewing quantum mechanics as an emergent theory requires a better understanding of all this. In this work we aim at a very modest goal, not quantum mechanics as thermodynamics, not yet, but the thermodynamics of quantum systems, or quantum thermodynamics. We will show why even with this minimal demand, there are many new issues which need be addressed and new rules formulated. The thermodynamics of small quantum many-body systems strongly coupled to a heat bath at low temperatures with non-Markovian behavior contains elements, such as quantum coherence, correlations, entanglement and fluctuations, that are not well recognized in traditional thermodynamics, built on large systems vanishingly weakly coupled to a non-dynamical reservoir. For quantum thermodynamics at strong coupling, one needs to reexamine the meaning of the thermodynamic functions, the viability of the thermodynamic relations and the validity of the thermodynamic laws anew. After a brief motivation, this paper starts with a short overview of the quantum formulation based on Gelin & Thoss and Seifert. We then provide a quantum formulation of Jarzynski’s two representations. We show how to construct the operator thermodynamic potentials, the expectation values of which provide the familiar thermodynamic variables. Constructing the operator thermodynamic functions and verifying or modifying their relations is a necessary first step in the establishment of a viable thermodynamics theory for

We present a set of benchmark calculations for the Kohn-Sham elastic transmission function of five representative single-molecule junctions. The transmission functions are calculated using two different densityfunctional theory methods, namely an ultrasoft pseudopotential plane-wave code...

A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn’s method and Löwdin method such that each Wannier function is localized at a Planck cell. With these Wannier functions one can map a wave function unitarily onto phase space. Various examples are used to illustrate our method and compare it to Wigner function. The advantage of our method is that it can smooth out the oscillations in wave functions without losing any information and is potentially a better tool in studying quantum-classical correspondence. In addition, we point out that our method can be used for time-frequency analysis of signals.

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability densityfunctions of systems of stochastic partial

Starting from Newton's equations of motion, we derive a dynamical densityfunctional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium densityfunctional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We show that when the isothermal compressibility is small, the DDFT generates the correct value for the speed of sound in a dense liquid. We also interpret the theory as a dynamical equation for a coarse grained fluid density and show that the theory can be used (making further approximations) to derive the standard mode coupling theory that is used to describe the glass transition. The present theory should provide a useful starting point for describing the dynamics of inhomogeneous atomic fluids

.... These data are gained by quantitating the number of microvessels in "hot spots" of high-density tumor vasculature, implying that such hot spots have functional significance in the process of metastasis...

Full Text Available By considering the effects of stress fields coming from lattice distortion as well as charge fields coming from line charges at edge dislocation cores on radiative recombination of exciton, a model of carriers’ radiative and non-radiative recombination has been established in GaN-based semiconductors with certain dislocation density. Using vector average of the stress fields and the charge fields, the relationship between dislocation density and the internal quantum efficiency (IQE is deduced. Combined with related experimental results, this relationship is fitted well to the trend of IQEs of bulk GaN changing with screw and edge dislocation density, meanwhile its simplified form is fitted well to the IQEs of AlGaN multiple quantum well LEDs with varied threading dislocation densities but the same light emission wavelength. It is believed that this model, suitable for different epitaxy platforms such as MOCVD and MBE, can be used to predict to what extent the luminous efficiency of GaN-based semiconductors can still maintain when the dislocation density increases, so as to provide a reasonable rule of thumb for optimizing the epitaxial growth of GaN-based devices.

We present a simple, classical densityfunctional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer densityfunctional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.

Five recent results from D0 which either impact or have the potential to impact on uncertainties in parton densityfunctions are presented. Many analyses at D0 are sensitive to the modeling of the partonic structure of the proton. When theoretical and experimental uncertainties are well controlled there exists the possibility for additional constraints on parton densityfunctions (PDF). Five measurements are presented which either have already been included in global parton fits or have the potential to contribute in the future.

The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is ''made'' of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.

Every approach to quantum mechanics postulating some kind of primitive ontology (e.g., Bohmian particles, a mass density field or flash-like collapse events) faces the challenge of clarifying the ontological status of the wave function. More precisely, one needs to spell out in what sense the wave function ''governs'' the behaviour of the primitive ontology, such that the empirical predictions of standard quantum mechanics are recovered. For Bohmian mechanics, this challenge has been addressed in recent papers by Belot and Esfeld et al. In my talk, I do the same for the matter density version of the Ghirardi-Rimini-Weber theory (GRWm). Doing so will highlight relevant similarities and differences between Bohmian mechanics and GRWm. The differences are a crucial element in the evaluation of the relative strengths and weaknesses of the two approaches, while the similarities can shed light on general characteristics of the primitive ontology approach, as opposed to other interpretative approaches to quantum mechanics.

The impact of the surface reconstruction of the density distribution and photoluminescence of silicon quantum dots (QDs) embedded in a silicon oxide matrix (SiO x ) has been studied. Annealing treatments carried out on the as-deposited samples provoked the effusion of hydrogen species. Moreover, depending on the surrounding density and coalescence of QDs, they resulted in a change in the average size of the particles depending on the initial local environment. The shift in the luminescence spectra all over the visible region (blue, green and red) shows a strong dependence on the resultant change in the size and/or the passivation environment of QDs. Densityfunctional theoretical (DFT) calculations support this fact and explain the possible electronic transitions (HOMO-LUMO gap) involved. Passivation in the presence of oxygen species lowers the band gap of Si 29 and Si 35 nanoclusters up to 1.7 eV, whereas, surface passivation in the environment of hydrogen species increases the band gap up to 4.4 eV. These results show a good agreement with the quantum confinement model described in this work and explain the shift in the luminescence all over the visible region. The results reported here offer vital insight into the mechanism of emission from silicon quantum dots which has been one of the most debated topics in the last two decades. QDs with multiple size distribution in different local environments (band gap) observed in this work could be used for the fabrication of light emission diodes (LEDs) or shift-conversion thin films in third generation efficient tandem solar cells for the maximum absorption of the solar spectrum in different wavelength regions.

In the first part of this work we extract the algebraic structure behind the method of the influence functional in the context of dissipative quantum mechanics. Special emphasis was put on the transition from a quantum mechanical description to a classical one, since it allows a deeper understanding of the measurement-process. This is tightly connected with the transition from a microscopic to a macroscopic world where the former one is described by the rules of quantum mechanics whereas the latter follows the rules of classical mechanics. In addition we show how the results of the influence functional method can be interpreted as a stochastical process, which in turn allows an easy comparison with the well known time development of a quantum mechanical system by use of the Schroedinger equation. In the following we examine the tight-binding approximation of models of which their hamiltionian shows discrete eigenstates in position space and where transitions between those states are suppressed so that propagation either is described by tunneling or by thermal activation. In the framework of dissipative quantum mechanics this leads to a tremendous simplification of the effective description of the system since instead of looking at the full history of all paths in the path integral description, we only have to look at all possible jump times and the possible corresponding set of weights for the jump direction, which is much easier to handle both analytically and numerically. In addition we deal with the mapping and the connection of dissipative quantum mechanical models with ones in quantum field theory and in particular models in statistical field theory. As an example we mention conformal invariance in two dimensions which always becomes relevant if a statistical system only has local interaction and is invariant under scaling. (orig.)

In a recent work, March has considered the quantum-mechanical system of an arbitrary number of closed electronic shells around an atomic nucleus of charge Z a e. March has assumed that the shells are filled by noninteracting electrons, moving in the bare Coulomb potential energy of V(r) = -Z a e 2 /r. In this framework, the basic quantity is the total electron (number) density ρ(r), built by summing the (number) density ρ n (r) of the nth closed electronic shell over the principal quantum number n. March has shown that Kato's theorem, (∂ρ(r)/∂r) r=0 = -(2Z a /a 0 )ρ (r = 0), with a 0 = ℎ 2 /me 2 , is amenable to a spatially dependent generalization that can be expressed by ∂ρ(r)/∂r = -(2Z a /a 0 )ρ s (r), where ρ s (r) is the s-state contribution from the n closed electronic shells to ρ(r). The present work investigates the spatially dependent generalization of Kato's theorem for the Ne atom by making use of a variational density-functional approach and adopting several expressions for the kinetic-energy functional of the electrons. The intriguing question of identifying the best kinetic-energy functional is raised and discussed

We propose densityfunctional theory for polymeric fluids in two dimensions. The approach is based on Wertheim’s first order thermodynamic perturbation theory (TPT) and closely follows densityfunctional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys . 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT. (paper)

The 'locality hypothesis' in density-functional theory (DFT), implying that the functional derivative is equivalent to a multiplicative local function, forms the basis of models of Kohn-Sham type. This has been generally accepted by the community since the advent of the model, and has later been formally proved for a large class of functionals. The hypothesis has recently been questioned by Nesbet [Phys. Rev. A 58, R12 (1998) and Phys. Rev. A 65, 010502 (2001)], who claims that it fails for the kinetic-energy functional for a system with more than two noninteracting electrons with a nondegenerate ground state. This conclusion has been questioned by Gal [Phys. Rev. A 62, 044501 (2000)] and by Holas and March [Phys. Rev. A 64, 016501 (2001)]. We claim that the arguments of Nesbet are incorrect, since the orbital functional used for the kinetic energy is not a unique functional of the total density in the domain of unnormalized orbitals. We have demonstrated that with a proper definition of the kinetic energy, which is a unique densityfunctional also in the unnormalized region, the derivative can be represented by a single local multiplicative function for all v-representable densities. Therefore, we consider the controversy connected with the issue raised by Nesbet as resolved. We believe that the proof of the differentiability given here can be extended to larger groups of DFT functionals, and works along these lines are in progress

In a recent paper, Nesbet [Phys. Rev. A 65, 010502(R) (2001)] has proposed dropping ''the widespread but unjustified assumption that the existence of a ground-state densityfunctional for the kinetic energy, T s [ρ], of an N-electron system implies the existence of a density-functional derivative, δT s [ρ]/δρ(r), equivalent to a local potential function,'' because, according to his arguments, this derivative 'has the mathematical character of a linear operator that acts on orbital wave functions'. Our Comment demonstrates that the statement called by Nesbet an 'unjustified assumption' happens, in fact, to be a rigorously proven theorem. Therefore, his previous conclusions stemming from his different view of this derivative, which undermined the foundations of density-functional theory, can be discounted

We construct a density-functional formalism adapted to uniform external magnetic fields that is intermediate between conventional densityfunctional theory and Current-DensityFunctional Theory (CDFT). In the intermediate theory, which we term linear vector potential-DFT (LDFT), the basic variables are the density, the canonical momentum, and the paramagnetic contribution to the magnetic moment. Both a constrained-search formulation and a convex formulation in terms of Legendre-Fenchel transformations are constructed. Many theoretical issues in CDFT find simplified analogs in LDFT. We prove results concerning N-representability, Hohenberg-Kohn-like mappings, existence of minimizers in the constrained-search expression, and a restricted analog to gauge invariance. The issue of additivity of the energy over non-interacting subsystems, which is qualitatively different in LDFT and CDFT, is also discussed.

In this paper, we propose a simple neural net that requires only $O(nlog_2k)$ number of qubits and $O(nk)$ quantum gates: Here, $n$ is the number of input parameters, and $k$ is the number of weights applied to these parameters in the proposed neural net. We describe the network in terms of a quantum circuit, and then draw its equivalent classical neural net which involves $O(k^n)$ nodes in the hidden layer. Then, we show that the network uses a periodic activation function of cosine values o...

The author discusses multiconfigurational Green's function techniques and generalizations. In particular he is interested in developing and applying these techniques for isolated atoms and small molecules. Furthermore, he develops formalisms that are fairly clear, accurate, and capable of being applied to open-shell and highly-correlated systems as well as to closed-shell systems with little electronic correlation. The two kinds of Green's functions that this article discusses are the single-particle Green's function and the retarded two-time Green's function in the energy representation. The poles of the former give the ionization potentials and electron affinities while the poles of the latter give the excitation energies. The multiconfigurational approximations are known as the multiconfigurational electron propagator (MCEP) and the multiconfigurational time-dependent Hartree-Fock (MCTDHF) (also known as the multiconfigurational random phase approximation (MCRPA) or the multiconfigurational linear response), respectively. 44 references

A method for directly patching exchange-correlation (XC) potentials in materials is derived. The electron density of a system is partitioned into subsystem densities by dividing its Kohn-Sham (KS) potential among the subsystems. Inside each subsystem, its projected KS potential is required to become the total system's KS potential. This requirement, together with the nearsightedness principle of electronic matters, ensures that the electronic structures inside subsystems can be good approximations to the total system's electronic structure. The nearsightedness principle also ensures that subsystem densities could be well localized in their regions, making it possible to use high-level methods to invert the XC potentials for subsystem densities. Two XC patching methods are developed. In the local XC patching method, the total system's XC potential is improved in the cluster region. We show that the coupling between a cluster and its environment is important for achieving a fast convergence of the electronic structure in the cluster region. In the global XC patching method, we discuss how to patch the subsystem XC potentials to construct the XC potential in the total system, aiming to scale up high-level quantum mechanics simulations of materials. Proof-of-principle examples are given.

We demonstrate that the thermodynamics of one-dimensional Lieb-Liniger bosons can be accurately calculated in analytic fashion using the polylog function in the framework of the thermodynamic Bethe ansatz. The approach does away with the need to numerically solve the thermodynamic Bethe ansatz (Yang-Yang) equation. The expression for the equation of state allows the exploration of Tomonaga-Luttinger liquid physics and quantum criticality in an archetypical quantum system. In particular, the low-temperature phase diagram is obtained, along with the scaling functions for the density and compressibility. It has been shown recently by Guan and Ho (arXiv:1010.1301) that such scaling can be used to map out the criticality of ultracold fermionic atoms in experiments. We show here how to map out quantum criticality for Lieb-Liniger bosons. More generally, the polylog function formalism can be applied to a wide range of Bethe ansatz integrable quantum many-body systems which are currently of theoretical and experimental interest, such as strongly interacting multi-component fermions, spinor bosons and mixtures of bosons and fermions. (fast track communication)

The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and densityfunctional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for densityfunctional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.

By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator

We present a practical scheme for performing error estimates for density-functional theory calculations. The approach, which is based on ideas from Bayesian statistics, involves creating an ensemble of exchange-correlation functionals by comparing with an experimental database of binding energies...

We propose a second version of the van der Waals densityfunctional of Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], employing a more accurate semilocal exchange functional and the use of a large-N asymptote gradient correction in determining the vdW kernel. The predicted binding energy...

We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF) formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superxtremal case (with charge-to-mass ratio $\\alpha>1$), which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for $\\alpha^2 2$, and the uncertainty in t...

We describe some recent mathematical results in constructing computational methods that lead to the development of fast and accurate multiresolution numerical methods for solving quantum chemistry and nuclear physics problems based on DensityFunctional Theory (DFT). Using low separation rank representations of functions and operators in conjunction with representations in multiwavelet bases, we developed a multiscale solution method for integral and differential equations and integral transforms. The Poisson equation, the Schrodinger equation, and the projector on the divergence free functions provide important examples with a wide range of applications in computational chemistry, nuclear physics, computational electromagnetic and fluid dynamics. We have implemented this approach along with adaptive representations of operators and functions in the multiwavelet basis and low separation rank (LSR) approximation of operators and functions. These methods have been realized and implemented in a software package called Multiresolution Adaptive Numerical Evaluation for Scientific Simulation (MADNESS)

Perhaps the most important approximations to the electronic structure problem in quantum chemistry are those based on coupled cluster and densityfunctional theories. Coupled cluster theory has been called the ``gold standard'' of quantum chemistry due to the high accuracy that it achieves for weakly correlated systems. Kohn-Sham densityfunctionals based on semilocal approximations are, without a doubt, the most widely used methods in chemistry and material science because of their high accuracy/cost ratio. The root of the success of coupled cluster and densityfunctionals is their ability to efficiently describe the dynamic part of the electron correlation. However, both traditional coupled cluster and densityfunctional approximations may fail catastrophically when substantial static correlation is present. This severely limits the applicability of these methods to a plethora of important chemical and physical problems such as, e.g., the description of bond breaking, transition states, transition metal-, lanthanide- and actinide-containing compounds, and superconductivity. In an attempt to tackle this problem, nonstandard (single-reference) coupled cluster-based techniques that aim to describe static correlation have been recently developed: pair coupled cluster doubles (pCCD) and singlet-paired coupled cluster doubles (CCD0). The ability to describe static correlation in pCCD and CCD0 comes, however, at the expense of important amounts of dynamic correlation so that the high accuracy of standard coupled cluster becomes unattainable. Thus, the reliable and efficient description of static and dynamic correlation in a simultaneous manner remains an open problem for quantum chemistry and many-body theory in general. In this thesis, different ways to combine pCCD and CCD0 with densityfunctionals in order to describe static and dynamic correlation simultaneously (and efficiently) are explored. The combination of wavefunction and densityfunctional methods has a long

Full Text Available The choice of bandwidth is crucial to the kernel density estimation (KDE and kernel based regression. Various bandwidth selection methods for KDE and local least square regression have been developed in the past decade. It has been known that scale and location parameters are proportional to densityfunctionals ∫γ(xf2(xdx with appropriate choice of γ(x and furthermore equality of scale and location tests can be transformed to comparisons of the densityfunctionals among populations. ∫γ(xf2(xdx can be estimated nonparametrically via kernel densityfunctionals estimation (KDFE. However, the optimal bandwidth selection for KDFE of ∫γ(xf2(xdx has not been examined. We propose a method to select the optimal bandwidth for the KDFE. The idea underlying this method is to search for the optimal bandwidth by minimizing the mean square error (MSE of the KDFE. Two main practical bandwidth selection techniques for the KDFE of ∫γ(xf2(xdx are provided: Normal scale bandwidth selection (namely, “Rule of Thumb” and direct plug-in bandwidth selection. Simulation studies display that our proposed bandwidth selection methods are superior to existing density estimation bandwidth selection methods in estimating densityfunctionals.

We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions, with particular but non-exclusive reference to loop quantum cosmology (LQC). Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

The path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories of volume transitions is discussed, with particular but non-exclusive reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview of the possible two-point functions, pointing out the choices involved in their definitions, deriving their vertex expansions and the composition laws they satisfy. We clarify the origin and relations of different quantities previously defined in the literature, in particular the tie between definitions using a group averaging procedure and those in a deparametrized framework. Finally, we draw some conclusions about the physics of a single quantum universe (where there exist superselection rules on positive- and negative-frequency sectors and different choices of inner product are physically equivalent) and multiverse field theories where the role of these sectors and the inner product are reinterpreted.

Up to date, studies of the fractional quantum Hall effect (FQHE) states in the second Landau level have mainly been carried out in the high electron density regime, where the electron mobility is the highest. Only recently, with the advance of high quality low density MBE growth, experiments have been pushed to the low density regime [1], where the electron-electron interactions are strong and the Landau level mixing parameter, defined by κ = e2/εIB/ℏωe, is large. Here, lB = (ℏe/B)1/2 is the magnetic length and ωc = eB/m the cyclotron frequency. All other parameters have their normal meanings. It has been shown that a large Landau level mixing effect strongly affects the electron physics in the second Landau level [2].

A study of the photoluminescence from a four-period Cd{sub x}Hg{sub 1-x}Te multiple quantum well structure at 11 K as a function of excitation density is presented. High-resolution X-ray diffraction and transmission electron microscopy revealed that the quantum well structure is of high quality. This was supported by the narrow photoluminescence peak originating in the ground state electron - heavy hole transition, with a full width at half maximum of only 7.4 meV for an excitation density of 1.3 W/cm{sup 2}. When the excitation density was increased from 1.3 to 23.4 W/cm{sup 2}, the peak position was shifted toward higher energy by 2.6 meV and the full width at half maximum increased from 7.4 to 10.9 meV.

Physical unclonable functions (PUFs) are physical structures that are hard to clone and have a unique challenge-response behavior. The term PUF was coined by Pappu et al. in 2001. That work triggered a lot of interest, and since then a substantial number of papers has been written about the use of a

Densityfunctional theory provides a very powerful tool for a unified microscopic description of nuclei all over the periodic table. It is not only successful in reproducing bulk properties of nuclear ground states such as binding energies, radii, or deformation parameters, but it also allows the investigation of collective phenomena, such as giant resonances and rotational excitations. However, it is based on the mean field concept and therefore it has its limits. We discuss here two methods based based on covariant densityfunctional theory going beyond the mean field concept, (i) models with an energy dependent self energy allowing the coupling to complex configurations and a quantitative description of the width of giant resonances and (ii) methods of configuration mixing between Slater determinants with different deformation and orientation providing are very successful description of transitional nuclei and quantum phase transitions.

Densityfunctional tight binding (DFTB), which is ∼100-1000 times faster than full densityfunctional theory (DFT), has been used to simulate the structure and properties of protic ionic liquid (IL) ions, clusters of ions and the bulk liquid. Proton affinities for a wide range of IL cations and anions determined using DFTB generally reproduce G3B3 values to within 5-10 kcal/mol. The structures and thermodynamic stabilities of n -alkyl ammonium nitrate clusters (up to 450 quantum chemical atoms) predicted with DFTB are in excellent agreement with those determined using DFT. The IL bulk structure simulated using DFTB with periodic boundary conditions is in excellent agreement with published neutron diffraction data.

Orbital-free densityfunctional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical methodology. In this paper, we developed a conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent extended Thomas-Fermi problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster Na216 with a local pseudopotential demonstrate that the method is accurate and efficient. (c) 2004 American Institute of Physics.

We utilize excited state densityfunctional theory (eDFT) to study Rydberg states in atoms. We show both analytically and numerically that semilocal functionals can give quite reasonable Rydberg energies from eDFT, even in cases where time dependent densityfunctional theory (TDDFT) fails catastrophically. We trace these findings to the fact that in eDFT the Kohn-Sham potential for each state is computed using the appropriate excited state density. Unlike the ground state potential, which typically falls off exponentially, the sequence of excited state potentials has a component that falls off polynomially with distance, leading to a Rydberg-type series. We also address the rigorous basis of eDFT for these systems. Perdew and Levy have shown using the constrained search formalism that every stationary density corresponds, in principle, to an exact stationary state of the full many-body Hamiltonian. In the present context, this means that the excited state DFT solutions are rigorous as long as they deliver the minimum noninteracting kinetic energy for the given density. We use optimized effective potential techniques to show that, in some cases, the eDFT Rydberg solutions appear to deliver the minimum kinetic energy because the associated density is not pure state v-representable. We thus find that eDFT plays a complementary role to constrained DFT: The former works only if the excited state density is not the ground state of some potential while the latter applies only when the density is a ground state density.

We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of Keating et al. (2014) that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitrary hypergraphs. We test the optimality of our condition on the maximal degree for p-uniform hypergraphs that correspond to p-spin glass Hamiltonians acting on n distinguishable spin- 1/2 particles. At the critical threshold p = n{sup 1/2} we find a sharp classical-quantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory.

This paper provides a general overview of the methodology implemented in onetep (Order-N Electronic Total Energy Package), a parallel density-functional theory code for largescale first-principles quantum-mechanical calculations. The distinctive features of onetep are linear-scaling in both computational effort and resources, obtained by making well-controlled approximations which enable simulations to be performed with plane-wave accuracy. Titanium dioxide clusters of increasing size designed to mimic surfaces are studied to demonstrate the accuracy and scaling of onetep

We investigated the effects of strain on the electronic structures of InAsxP1-x using quantum mechanical densityfunctional theory calculations. The electronic band gap and electron effective mass decreased with the increase of the uniaxial tensile strain along the [0001] direction of wurtzite InAs0.75P0.25. Therefore, faster electron movements are expected. These theoretical results are in good agreement with the experimental measurements of InAs0.75P0.25 nanowire.

The physics of solvation, the interaction of water with solutes, plays a central role in chemistry and biochemistry, and it is essential for the very existence of life. Despite the central importance of water and the advent of the quantum theory early in the twentieth century, the link between the fundamental laws of physics and the observable properties of water remain poorly understood to this day. The central goal of this thesis is to develop a new formalism and framework to make the study of systems (solutes or surfaces) in contact with liquid water as practical and accurate as standard electronic structure calculations without the need for explicit averaging over large ensembles of configurations of water molecules. The thesis introduces a new form of densityfunctional theory for the ab initio description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. Using the new form of density-functional theory for the ab initio description of electronic systems in contact with a molecular liquid environment, the thesis then presents the first detailed study of the impact of a solvent on the surface chemistry of Cr2O3, the passivating layer of stainless steel alloys. In comparison to a vacuum, we predict that the presence of water has little impact on the adsorption of chloride ions to the oxygen-terminated surface but has a dramatic effect on the binding of hydrogen to that surface. A key ingredient of a successful joint densityfunctional theory is a good approximate functional for describing the solvent. We explore how the simplest examples of the best known class of approximate forms for the classical densityfunctional fail when applied directly to water. The thesis then presents a computationally efficient density-functional

In order to improve the rate of decrease of the IMSE for nonparametric kernel density estimators with nonrandom bandwidth beyond $O(n^{-4/5})$ all current methods must relax the constraint that the density estimate be a bona fide function, that is, be nonnegative and integrate to one. In this paper we show how to achieve similar improvement without relaxing any of these constraints. The method can also be applied for orthogonal series, adaptive orthogonal series, spline, jackknife, and other ...

During the last few years considerable effort has been devoted to deriving quantum transport equations for semiconductors under extreme conditions (high electric fields, spatial quantization in one or two directions). Here we review the results obtained with nonequilibrium Green function techniques as formulated by Baym and Kadanoff, or by Keldysh. In particular, the following topics will be discussed: (i) Systematic approaches to reduce the transport equation governing the correlation function to a transport equation for the Wigner function; (ii) Approximations reducing the nonmarkovian quantum transport equation to a numerically tractable form, and results for model semiconductors; (iii) Recent progress in extending the formalism to inhomogeneous systems; and (iv) Nonequilibrium screening. In all sections we try to direct the reader's attention to points where the present understanding is (at best) incomplete, and indicate possible lines for future work. (orig.)

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the

Background: The central depression of nucleonic density, i.e., a reduction of density in the nuclear interior, has been attributed to many factors. For instance, bubble structures in superheavy nuclei are believed to be due to the electrostatic repulsion. In light nuclei, the mechanism behind the density reduction in the interior has been discussed in terms of shell effects associated with occupations of s orbits. Purpose: The main objective of this work is to reveal mechanisms behind the formation of central depression in nucleonic densities in light and heavy nuclei. To this end, we introduce several measures of the internal nucleonic density. Through the statistical analysis, we study the information content of these measures with respect to nuclear matter properties. Method: We apply nuclear densityfunctional theory with Skyrme functionals. Using the statistical tools of linear least square regression, we inspect correlations between various measures of central depression and model parameters, including nuclear matter properties. We study bivariate correlations with selected quantities as well as multiple correlations with groups of parameters. Detailed correlation analysis is carried out for 34Si for which a bubble structure has been reported recently, 48Ca, and N =82 , 126, and 184 isotonic chains. Results: We show that the central depression in medium-mass nuclei is very sensitive to shell effects, whereas for superheavy systems it is firmly driven by the electrostatic repulsion. An appreciable semibubble structure in proton density is predicted for 294Og, which is currently the heaviest nucleus known experimentally. Conclusion: Our correlation analysis reveals that the central density indicators in nuclei below 208Pb carry little information on parameters of nuclear matter; they are predominantly driven by shell structure. On the other hand, in the superheavy nuclei there exists a clear relationship between the central nucleonic density and symmetry energy.

Two vertically stacked quantum dots that are electronically coupled, so called quantum dot molecules, are of great interest for the realization of solid state building blocks for quantum communication networks. We present a modified gradient approach to realize InAs quantum dot molecules with a low areal density so that single quantum dot molecules can be optically addressed. The individual quantum dot layers were prepared by solid source molecular beam epitaxy depositing InAs on GaAs(100). The bottom quantum dot layer has been grown without substrate rotation resulting in an In-gradient across the surface, which translated into a density gradient with low quantum dot density in a certain region of the wafer. For the top quantum dot layer, separated from the bottom quantum dot layer by a 6 nm thick GaAs barrier, various InAs amounts were deposited without an In-gradient. In spite of the absence of an In-gradient, a pronounced density gradient is observed for the top quantum dots. Even for an In-amount slightly below the critical thickness for a single dot layer, a density gradient in the top quantum dot layer, which seems to reproduce the density gradient in the bottom layer, is observed. For more or less In, respectively, deviations from this behavior occur. We suggest that the obvious influence of the bottom quantum dot layer on the growth of the top quantum dots is due to the strain field induced by the buried dots.

We give an overview of the fundamental concepts of densityfunctional theory. We give a careful discussion of the several densityfunctionals and their differentiability properties. We show that for nondegenerate ground states we can calculate the necessary functional derivatives by means of linear

Probability densityfunction (PDF) methods are extended to variable-density pressure-gradient-driven turbulence. We apply the new method to compute the joint PDF of density and velocity in a non-premixed binary mixture of different-density molecularly mixing fluids under gravity. The full time-evolution of the joint PDF is captured in the highly non-equilibrium flow: starting from a quiescent state, transitioning to fully developed turbulence and finally dissipated by molecular diffusion. High-Atwood-number effects (as distinguished from the Boussinesq case) are accounted for: both hydrodynamic turbulence and material mixing are treated at arbitrary density ratios, with the specific volume, mass flux and all their correlations in closed form. An extension of the generalized Langevin model, originally developed for the Lagrangian fluid particle velocity in constant-density shear-driven turbulence, is constructed for variable-density pressure-gradient-driven flows. The persistent small-scale anisotropy, a fundamentally 'non-Kolmogorovian' feature of flows under external acceleration forces, is captured by a tensorial diffusion term based on the external body force. The material mixing model for the fluid density, an active scalar, is developed based on the beta distribution. The beta-PDF is shown to be capable of capturing the mixing asymmetry and that it can accurately represent the density through transition, in fully developed turbulence and in the decay process. The joint model for hydrodynamics and active material mixing yields a time-accurate evolution of the turbulent kinetic energy and Reynolds stress anisotropy without resorting to gradient diffusion hypotheses, and represents the mixing state by the density PDF itself, eliminating the need for dubious mixing measures. Direct numerical simulations of the homogeneous Rayleigh-Taylor instability are used for model validation.

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called densityfunctional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum densityfunction. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called densityfunctional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum densityfunction. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.

We present a nonlocal kinetic-energy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exact calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. copyright 1996 The American Physical Society

The time evolution of the probability densityfunction (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P V (ρ)∝ρ –1.54 for the (volume-weighted) PDF and P M (ρ)∝ρ –0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.

This work is an attempt to go beyond the standard description of hot condensed matter using the well-known ''average atom model''. The first part describes a static model using ''Densityfunctional theory'' to calculate self-consistent coupled electron and ion density profiles of the plasma not restricted to a single average atomic sphere. In a second part, the results are used as ingredients for a many-body approach to electronic properties: the one-particle Green-function self-energy is calculated, from which shifted levels, populations and level-widths are deduced. Results for the Hydrogen plasma are reported, with emphasis on the 1s bound state

Limit lines used to define quantitative probabilistic safety goals can be categorized according to whether they are based on discrete pairs of event sequences and associated probabilities, on probability densityfunctions (pdf's), or on complementary cumulative densityfunctions (CCDFs). In particular, the concept of the well-known Farmer's line and its subsequent reinterpretations is clarified. It is shown that Farmer's lines are pdf's and, therefore, the overall risk (defined as the expected value of the pdf) that they represent can be easily calculated. It is also shown that the area under Farmer's line is proportional to probability, while the areas under CCDFs are generally proportional to expected value

Perturbation theory with respect to the electron-electron interaction leads to expressions for the exchange and correlation energies and potentials in terms of Kohn-Sham orbitals and Kohn-Sham eigenvalues. An exact open-quote exchange-only close-quote procedure for solids is introduced. Results for several semiconductors are presented. Perturbation theory expansions for the hardness of molecules and the bad gap of solids are given. Density-functional exchange and correlation energies for excited states are defined and a perturbation theory based Kohn-Sham formalism to treat excited states within density-functional theory is introduced

We present first results from a new parton shower event generator, D eductor . Anticipating a need for an improved treatment of parton color and spin, the structure of the generator is based on the quantumdensity matrix in color and spin space. So far, D eductor implements only a standard spin-averaged treatment of spin in parton splittings. Although D eductor implements an improved treatment of color, in this paper we present results in the standard leading color approximation so that we ca...

We present rst results from a new parton shower event generator, DEDUCTOR. Anticipating a need for an improved treatment of parton color and spin, the structure of the generator is based on the quantumdensity matrix in color and spin space. So far, DEDUCTOR implements only a standard spin-averaged treatment of spin in parton splittings. Although DEDUCTOR implements an improved treatment of color, in this paper we present results in the standard leading color approximation so that we can compare to the generator PYTHIA. The algorithms used incorporate a virtuality based shower ordering parameter and massive initial state bottom and charm quarks.

Full text: An experimentally realizable scheme is formulated which can test any quantum mechanical approach for calculating the arrival time distribution. This is specifically illustrated by using the modulus of the probability current density for calculating the arrival time distribution of spin-1/2 neutral particles at the exit point of a spin rotator (SR) which contains a constant magnetic field. Such a calculated time distribution is then used for evaluating the distribution of spin orientations along different directions for these particles emerging from the SR. Based on this, the result of spin measurement along any arbitrary direction for such an ensemble is predicted. (author)

New and simple numerical method is being reported to solve anharmonic oscillator problems. The method is setup to approach the real potential V(x) of the anharmonic oscillator system as a piecewise linear potential u(x) and to solve the Schrödinger equation of the system using the Airy function. Then, solutions continuity conditions lead to the energy quantification condition, and consequently, the energy eigenvalues. For testing purpose, the method was applied on the sextic and octic oscillators systems. The proposed method is found to be realistic, computationally simple, and having high degrees of accuracy. In addition, it can be applied to any form of potential. The results obtained by the proposed method were seen closely agreeing with results reached by other complicated methods.

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham densityfunctional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham densityfunctional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

The uniform electron gas and the hydrogen atom play fundamental roles in condensed matter physics and quantum chemistry. The former has an infinite number of electrons uniformly distributed over the neutralizing positively charged background, and the latter only one electron bound to the proton. The uniform electron gas was used to derive the local spin density approximation to the exchange-correlation functional that undergirds the development of the Kohn-Sham densityfunctional theory. We show here that the ground-state exchange-correlation energies of the hydrogen atom and many other 1- and 2-electron systems are modeled surprisingly well by a different local spin density approximation (LSDA0). LSDA0 is constructed to satisfy exact constraints but agrees surprisingly well with the exact results for a uniform two-electron density in a finite, curved three-dimensional space. We also apply LSDA0 to excited or noded 1-electron densities, where it works less well. Furthermore, we show that the localization of the exact exchange hole for a 1- or 2-electron ground state can be measured by the ratio of the exact exchange energy to its optimal lower bound.

Full Text Available Finite-temperature densityfunctional theory (DFT has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM.Warm-dense matter (WDM, ultra-fast matter (UFM, and high-energy density matter (HEDM may all be regarded as subclasses of WCM. Strong electron-electron, ion-ion and electron-ion correlation effects and partial degeneracies are found in these systems where the electron temperature Te is comparable to the electron Fermi energy EF. Thus, many electrons are in continuum states which are partially occupied. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge Zj. Quasi-equilibria with the ion temperature Ti ≠ Te are common. The ion subsystem in WCM can no longer be treated as a passive “external potential”, as is customary in T = 0 DFT dominated by solid-state theory or quantum chemistry. Many basic questions arise in trying to implement DFT for WCM. Hohenberg-Kohn-Mermin theory can be adapted for treating these systems if suitable finite-T exchange-correlation (XC functionals can be constructed. They are functionals of both the one-body electron density ne and the one-body ion densities ρj. Here, j counts many species of nuclei or charge states. A method of approximately but accurately mapping the quantum electrons to a classical Coulomb gas enables one to treat electron-ion systems entirely classically at any temperature and arbitrary spin polarization, using exchange-correlation effects calculated in situ, directly from the pair-distribution functions. This eliminates the need for any XC-functionals. This classical map has been used to calculate the equation of state of WDM systems, and construct a finite-T XC functional that is found to be in close agreement with recent quantum path-integral simulation data. In this review, current developments and concerns in finite-T DFT, especially in the context of non-relativistic warm

Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.

Full Text Available We investigate the Cosmic Censorship Conjecture by means of the horizon wave-function (HWF formalism. We consider a charged massive particle whose quantum mechanical state is represented by a spherically symmetric Gaussian wave-function, and restrict our attention to the superextremal case (with charge-to-mass ratio α>1, which is the prototype of a naked singularity in the classical theory. We find that one can still obtain a normalisable HWF for α22, and the uncertainty in the location of the horizon blows up at α2=2, signalling that such an object is no more well-defined. This perhaps implies that a quantum Cosmic Censorship might be conjectured by stating that no black holes with charge-to-mass ratio greater than a critical value (of the order of 2 can exist.

We present an implementation of the linear density response function within the projector-augmented wave method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single...... functions of Si, C, SiC, AlP, and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001...

Quantum dynamics of a particle coupled to a fermionic environment is considered, with particular emphasis on the formulation of macroscopic quantum phenomena. The framework is based on a path integral formalism for the real-time density matrix. After integrating out of the fermion variables of the environment, they embed the whole environmental effects on the particle into the so-called influence functional in analogy to Feynman and Vernon's initial work. They then show that to the second order of the coupling constant, the exponent of the influence functional is in exact agreement with that due to a linear dissipative environment (boson bath). Having obtained this, they turn to a specific model in which the influence functional can be exactly evaluated in a long-term limit (long compared to the inverse of the cutoff frequency of the environmental spectrum). In this circumstance, they mainly address their attention to the quantum mechanical representation of the system-plus-environment from the known classical properties of the particle. It is shown that, in particular, the equivalence between the fermion bath and the boson bath is generally correct for a single-channel coupling provided they make a simple mapping between the nonlinear interaction functions of the baths. Finally, generalizations of the model to more complicated situations are discussed and significant applications and connections to certain practically interesting problems are mentioned

We investigate the domain of validity of previously proposed analytical wave functions for atomic quantum-defect theory. This is done by considering the fine-structure splitting of alkali-metal and singly ionized alkaline-earth atoms. The Lande formula is found to be naturally incorporated. A supersymmetric-type integer is necessary for finite results. Calculated splittings correctly reproduce the principal features of experimental values for alkali-like atoms

Light is a quantum electrodynamic entity and hence bundles of rays must be describable in this framework. The duality in the description of elementary optical phenomena is demonstrated in terms of two-point correlation functions and in terms of collections of light rays. The generalizations necessary to deal with two-slit interference and diffraction by a rectangular slit are worked out and the usefulness of the notion of rays of darkness illustrated. 10 references.

We numerically investigate the effect of the wetting-layer (WL) density of states on the gain and phase recovery dynamics of quantum-dot semiconductor optical amplifiers in both electrical and optical pumping schemes by solving 1088 coupled rate equations. The temporal variations of the ultrafast gain and phase recovery responses at the ground state (GS) are calculated as a function of the WL density of states. The ultrafast gain recovery responses do not significantly depend on the WL density of states in the electrical pumping scheme and the three optical pumping schemes such as the optical pumping to the WL, the optical pumping to the excited state ensemble, and the optical pumping to the GS ensemble. The ultrafast phase recovery responses are also not significantly affected by the WL density of states except the optical pumping to the WL, where the phase recovery component caused by the WL becomes slowed down as the WL density of states increases. (paper)

Recently, an intriguing solution to obtain better color purity has been to introduce inorganic emissive quantum dots (QDs) into an otherwise OLED structure. The emphasis of this chapter is to present a simple discussion of the first attempts to fabricate high-density, pixelated (quarter video graphics array (QVGA) format), monochromatic and RGB quantum dots light-emitting diodes (QDLEDs), where inkjet printing is used to deposit the light-emitting layer of QDs. It shows some of the factors that have to be considered in order to achieve the desired accuracy and printing quality. The successful operation of the RGB printed devices indicates the potential of the inkjet printing approach in the fabrication of full-color QDLEDs for display application. However, further optimization of print quality is still needed in order to eliminate the formation of pinholes, thus maximizing energy transfer from organic layers to the QDs and in turn increasing the performance of the devices. Controlled Vocabulary Terms: ink jet printing; LED displays; LED lamps; organic light emitting diodes; quantum dots

Recent developments/efforts to understand aspects of the brain function at the {\\em sub-neural} level are discussed. MicroTubules (MTs) participate in a wide variety of dynamical processes in the cell especially in bioinformation processes such as learning and memory, by possessing a well-known binary error-correcting code with 64 words. In fact, MTs and DNA/RNA are unique cell structures that possess a code system. It seems that the MTs' code system is strongly related to a kind of ``Mental Code" in the following sense. The MTs' periodic paracrystalline structure make them able to support a superposition of coherent quantum states, as it has been recently conjectured by Hameroff and Penrose, representing an external or mental order, for sufficient time needed for efficient quantum computing. Then the quantum superposition collapses spontaneously/dynamically through a new, string-derived mechanism for collapse proposed recently by Ellis, Mavromatos, and myself. At the moment of collapse, organized quantum exo...

In this work, the state-of-art densityfunctional theory is employed to study the structural, electronic and magnetic properties of samarium nitride (SmN). We have performed calculation for both ferromagnetic and antiferromagnetic states in rock-salt phase. The calculated results of optimized lattice parameter and magnetic moment agree well with the available experimental and theoretical values. From energy band diagram and electronic density of states, we observe a half-metallic behaviour in FM phase of rock salt SmN in while metallicity in AFM I and AFM III phases. We present and discuss our current understanding of the possible half-metallicity together with the magnetic ordering in SmN. The calculated phonon dispersion curves shows dynamical stability of the considered structures. The phonon density of states and Eliashberg functional have also been analysed to understand the superconductivity in SmN.

We apply the KIDS (Korea: IBS-Daegu-Sungkyunkwan) nuclear energy densityfunctional model, which is based on the Fermi momentum expansion, to the study of properties of lj-closed nuclei. The parameters of the model are determined by the nuclear properties at the saturation density and theoretical calculations on pure neutron matter. For applying the model to the study of nuclei, we rely on the Skyrme force model, where the Skyrme force parameters are determined through the KIDS energy densityfunctional. Solving Hartree-Fock equations, we obtain the energies per particle and charge radii of closed magic nuclei, namely, 16O, 28O, 40Ca, 48Ca, 60Ca, 90Zr, 132Sn, and 208Pb. The results are compared with the observed data and further improvement of the model is shortly mentioned.

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high Tc superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.

In contrast to metals with weak disorder, the resistivity of weakly pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high T_{c} superconductors. We conclude by speculating on the possible relevance of unstable, semilocally critical CDW states to the strange metallic region.

We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).

Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal. Nevertheless, it has been shown that if there is a classical algorithm that can simulate IQP efficiently, the polynomial hierarchy collapses to the third level, which is highly implausible. However, the origin of the classical intractability is still less understood. Here we establish a relationship between IQP and computational complexity of calculating the imaginary-valued partition functions of Ising models. We apply the established relationship in two opposite directions. One direction is to find subclasses of IQP that are classically efficiently simulatable by using exact solvability of certain types of Ising models. Another direction is applying quantum computational complexity of IQP to investigate (im)possibility of efficient classical approximations of Ising partition functions with imaginary coupling constants. Specifically, we show that a multiplicative approximation of Ising partition functions is #P-hard for almost all imaginary coupling constants even on planar lattices of a bounded degree. (paper)

Solid surfaces are used extensively as catalysts throughout the chemical industry, in the energy sector, and in environmental protection. Recently, densityfunctional theory has started providing new insight into the atomic-scale mechanisms of heterogeneous catalysis, helping to interpret the large...

We propose a method to characterize and quantify multipartite entanglement for pure states. The method hinges upon the study of the probability densityfunction of bipartite entanglement and is tested on an ensemble of qubits in a variety of situations. This characterization is also compared to several measures of multipartite entanglement

A graph representation of terms in the gradient expansion of the kinetic energy densityfunctional is presented. They briefly discuss the implications of the virial theorem for the graph structure and relations between possible graphs at a given order of expansion

Applications of classical densityfunctional theory (DFT) to soft matter systems like colloids, liquid crystals and polymer solutions are discussed with a focus on the freezing transition and on nonequilibrium Brownian dynamics. First, after a brief reminder of equilibrium densityfunctional theory, DFT is applied to the freezing transition of liquids into crystalline lattices. In particular, spherical particles with radially symmetric pair potentials will be treated (like hard spheres, the classical one-component plasma or Gaussian-core particles). Second, the DFT will be generalized towards Brownian dynamics in order to tackle nonequilibrium problems. After a general introduction to Brownian dynamics using the complementary Smoluchowski and Langevin pictures appropriate for the dynamics of colloidal suspensions, the dynamical densityfunctional theory (DDFT) will be derived from the Smoluchowski equation. This will be done first for spherical particles (e.g. hard spheres or Gaussian-cores) without hydrodynamic interactions. Then we show how to incorporate hydrodynamic interactions between the colloidal particles into the DDFT framework and compare to Brownian dynamics computer simulations. Third orientational degrees of freedom (rod-like particles) will be considered as well. In the latter case, the stability of intermediate liquid crystalline phases (isotropic, nematic, smectic-A, plastic crystals etc) can be predicted. Finally, the corresponding dynamical extension of densityfunctional theory towards orientational degrees of freedom is proposed and the collective behaviour of "active" (self-propelled) Brownian particles is briefly discussed.

An all-electron scalar relativistic calculation on the adsorption of hydrogen molecule onto small copper clusters has been performed by using densityfunctional theory with the generalized gradient approximation (GGA) at PW91 level. Our results reveal that after adsorption of H2 molecule, the Cu-Cu interaction is ...

A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of densityfunctional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few ...

The structure of low-energy collective states in the neutron-rich nucleus 44 S is analyzed using a microscopic collective Hamiltonian model based on energy densityfunctionals (EDFs). The calculated triaxial energy map, low-energy spectrum and corresponding probability distributions indicate a coexistence of prolate and oblate shapes in this nucleus.

Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply densityfunctionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark aga...

Using arguments from two-dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density-correlation function for coupling l and 1/l, where l is an integer. We present overwhelming evidence that the conjecture is indeed correct

Using arguments from two dimensional Yang-Mills theory and the collective coordinate formulation of the Calogero-Sutherland model, we conjecture the dynamical density correlation function for coupling l and 1/l, where l is an integer. We present overwhelming evidence that the conjecture is indeed correct.

We are looking for a material which possesses the required properties as demanded for technological applications. For this we have to repeat the preparation of the appropriate materials and its characterizations. So, before proceeding to experiments, one can study on computer generated structure and predict the properties of the desired material. To do this, a concept of DensityFunctional Theory comes out. (paper)

Provides an account of the fundamental principles of the density-functional theory of the electronic structure of matter and its applications to atoms and molecules. This book contains a discussion of the chemical potential and its derivatives. It is intended for physicists, chemists, and advanced students in chemistry.

This work investigates the surfactant effect on exposed and buried InAs quantum dots (QDs) by incorporating Sb into the QD layers with various Sb beam equivalent pressures (BEPs). Secondary ion mass spectroscopy shows the presence of Sb in the exposed and buried QD layers with the Sb intensity in the exposed layer substantially exceeding that in the buried layer. Incorporating Sb can reduce the density of the exposed QDs by more than two orders of magnitude. However, a high Sb BEP yields a surface morphology with a regular periodic structure of ellipsoid terraces. A good room-temperature photoluminescence (PL) at ˜1600 nm from the exposed QDs is observed, suggesting that the Sb incorporation probably improves the emission efficiency by reducing the surface recombination velocity at the surface of the exposed QDs. Increasing Sb BEP causes a blueshift of the emission from the exposed QDs due to a reduction in the dot height as suggested by atomic force microscopy. Increasing Sb BEP can also blueshift the ˜1300 nm emission from the buried QDs by decreasing the dot height. However, a high Sb BEP yields a quantum well-like PL feature formed by the clustering of the buried QDs into an undulated planar layer. These results indicate a marked Sb surfactant effect that can be used to control the density, shape, and luminescence of the exposed and buried QDs.

The relationship between the densities of ground-state wave functions (i.e., the minimizers of the Rayleigh-Ritz variation principle) and the ground-state densities in density-functional theory (i.e., the minimizers of the Hohenberg-Kohn variation principle) is studied within the framework of convex conjugation, in a generic setting covering molecular systems, solid-state systems, and more. Having introduced admissible densityfunctionals as functionals that produce the exact ground-state energy for a given external potential by minimizing over densities in the Hohenberg-Kohn variation principle, necessary and sufficient conditions on such functionals are established to ensure that the Rayleigh-Ritz ground-state densities and the Hohenberg-Kohn ground-state densities are identical. We apply the results to molecular systems in the Born-Oppenheimer approximation. For any given potential v ∈ L(3/2)(ℝ(3)) + L(∞)(ℝ(3)), we establish a one-to-one correspondence between the mixed ground-state densities of the Rayleigh-Ritz variation principle and the mixed ground-state densities of the Hohenberg-Kohn variation principle when the Lieb density-matrix constrained-search universal densityfunctional is taken as the admissible functional. A similar one-to-one correspondence is established between the pure ground-state densities of the Rayleigh-Ritz variation principle and the pure ground-state densities obtained using the Hohenberg-Kohn variation principle with the Levy-Lieb pure-state constrained-search functional. In other words, all physical ground-state densities (pure or mixed) are recovered with these functionals and no false densities (i.e., minimizing densities that are not physical) exist. The importance of topology (i.e., choice of Banach space of densities and potentials) is emphasized and illustrated. The relevance of these results for current-density-functional theory is examined.

We consider generating functionals for computing correlators in quantum field theories with random potentials. Examples of such theories include cosmological systems in context of the string theory landscape (e.g. cosmic inflation) or condensed matter systems with quenched disorder (e.g. spin glass). We use the so-called replica trick to define two different generating functionals for calculating correlators of the quantum fields averaged over a given distribution of random potentials. The first generating functional is appropriate for calculating averaged (in-out) amplitudes and involves a single replica of fields, but the replica limit is taken to an (unphysical) negative one number of fields outside of the path integral. When the number of replicas is doubled the generating functional can also be used for calculating averaged probabilities (squared amplitudes) using the in-in construction. The second generating functional involves an infinite number of replicas, but can be used for calculating both in-out and in-in correlators and the replica limits are taken to only a zero number of fields. We discuss the formalism in details for a single real scalar field, but the generalization to more fields or to different types of fields is straightforward. We work out three examples: one where the mass of scalar field is treated as a random variable and two where the functional form of interactions is random, one described by a Gaussian random field and the other by a Euclidean action in the field configuration space.

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

This book is on approximation methods and applications of Quantal DensityFunctional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional densityfunctional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces. (orig.)

The linear chain of hydrogen atoms, a basic prototype for the transition from a metal to Mott insulator, is studied with a recent densityfunctional theory model functional for nondynamic and strong correlation. The computed cohesive energy curve for the transition agrees well with accurate literature results. The variation of the electronic structure in this transition is characterized with a densityfunctional descriptor that yields the atomic population of effectively localized electrons. These new methods are also applied to the study of the Peierls dimerization of the stretched even-spaced Mott insulator to a chain of H 2 molecules, a different insulator. The transitions among the two insulating states and the metallic state of the hydrogen chain system are depicted in a semiquantitative phase diagram. Overall, we demonstrate the capability of studying strongly correlated materials with a mean-field model at the fundamental level, in contrast to the general pessimistic view on such a feasibility.

Ethylene-dinitrobenzoyl (EDNB) linked to graphene oxide has been shown to improve the performance of graphene/polymer organic photovoltaics. Its binding conformation on graphene, however, is not yet clear, nor have its effects on work function and optical absorption been explored more generally for graphene quantum dots. In this report, we clarify the linkage of EDNB to GQDs from first principles and show that the binding of the molecule increases the work function of graphene, while simultaneously modifying its absorption in the ultraviolet region.

Ethylene-dinitrobenzoyl (EDNB) linked to graphene oxide has been shown to improve the performance of graphene/polymer organic photovoltaics. Its binding conformation on graphene, however, is not yet clear, nor have its effects on work function and optical absorption been explored more generally for graphene quantum dots. In this report, we clarify the linkage of EDNB to GQDs from first principles and show that the binding of the molecule increases the work function of graphene, while simultaneously modifying its absorption in the ultraviolet region.

The quantum-mechanical Green's function is derived for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field. (Author) [pt

It is derived the quantum-mechanical Green's function for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic-oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field

Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that the variance, related to the second functional variation of the effective action, requires a further regularization and that the relative regularized variance turns out to be 2/N, where N is the number of the fields, thus being independent of the dimension D. Some illustrating examples are worked through. The issue of the stress tensor is also briefly addressed

The relative merits of current-spin-density- and spin-density-functional theory are investigated for solids treated within the exact-exchange-only approximation. Spin-orbit splittings and orbital magnetic moments are determined at zero external magnetic field. We find that for magnetic (Fe, Co......, and Ni) and nonmagnetic (Si and Ge) solids, the exact-exchange current-spin-densityfunctional approach does not significantly improve the accuracy of the corresponding spin-densityfunctional results....

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular densityfunctional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard densityfunctional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability densityfunctions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

The densityfunctional theory is derived from a cluster expansion by truncating the higher-order correlations in one and only one term in the kinetic energy. The formulation allows self-consistent calculation of the exchange correlation effect without imposing additional assumptions to generalize the local density approximation. The pair correlation is described as a two-body collision of bound-state electrons, and modifies the electron- electron interaction energy as well as the kinetic energy. The theory admits excited states, and has no self-interaction energy.

Maitra, Neepa T. [Department of Physics and Astronomy, Hunter College and the Physics Program at the Graduate Center of the City University of New York, 695 Park Avenue, New York, New York 10065 (United States)

2016-06-14

In the thirty-two years since the birth of the foundational theorems, time-dependent densityfunctional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.

I propose a simple and manageable method that allows for deriving coupling constants of model energy densityfunctionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results. (letter)

The description of exotic nuclear systems and phenomena requires a detailed understanding of all channels of densityfunctional theories. The role of time-odd mean fields, their evidence in experiment, and an accurate description of these fields are subject of current interest. Recent studies advanced the understanding of these fields in energy densityfunctional theories based on the Skyrme force [1,2]. Time-odd mean fields are related to nuclear magnetism in covariant densityfunctional (CDF) theories [3]. They arise from space-like components of vector mesons and Lorentz invariance requires that their coupling strengths are identical to that of time-like components. There were only few limited efforts to understand the role of time-odd mean fields in covariant densityfunctional theory [4,5]. For example, the microscopic role of nuclear magnetism and its impact on rotational properties of nuclei has been studied in Ref. [5]. It is known that time-odd mean fields modify the angular momentum content of the single-particle orbitals and thus the moments of inertia, effective alignments, alignment gains at the band crossings and other physical observables. We aim on more detailed and systematic understanding of the role of time-odd mean fields in covariant densityfunctional theory. This investigation covers both rotating and non-rotating systems. It is shown that contrary to the Skyrme energy densityfunctionals time-odd mean fields of CDF theory always provide additional binding in the systems with broken time-reversal symmetry (rotating nuclei, odd mass nuclei). This additional binding increases with spin and has its maximum exactly at the terminating state [6], where it can reach several MeV. The impact of time-odd mean fields on the properties of rotating systems has been studied in a systematic way (as a function of particle number and deformation) across the nuclear chart [7]. In addition, this contribution extends these studies to non-rotating systems such as

The structure of Poisson Lie groups on a simple compact group are parametrized by pairs (a, u), where aelement ofR, uelement ofΛ 2 f R , and f R is a real Cartan subalgebra of complexification of Lie algebra of the group in question. In the present article the description of the symplectic leaves for all pairs (a, u) is given. Also, the corresponding quantized algebras of functions are constructed and their irreducible representations are described. In the course of investigation Schubert cells and quantum tori appear. At the end of the article the quantum analog of the Weyl group is constructed and some of its applications, among them the formula for the universal R-matrix, are given. (orig.)

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier-Stokes equations, originally derived by Landau and Lifshitz

During the last 20 years computer simulations based on a quantum-mechanical description of the interactions between electrons and atomic nuclei have developed an increasingly important impact on materials science, not only in promoting a deeper understanding of the fundamental physical phenomena, but also enabling the computer-assisted design of materials for future technologies. The backbone of atomic-scale computational materials science is density-functional theory (DFT) which allows us to cast the intractable complexity of electron-electron interactions into the form of an effective single-particle equation determined by the exchange-correlation functional. Progress in DFT-based calculations of the properties of materials and of simulations of processes in materials depends on: (1) the development of improved exchange-correlation functionals and advanced post-DFT methods and their implementation in highly efficient computer codes, (2) the development of methods allowing us to bridge the gaps in the temperature, pressure, time and length scales between the ab initio calculations and real-world experiments and (3) the extension of the functionality of these codes, permitting us to treat additional properties and new processes. In this paper we discuss the current status of techniques for performing quantum-based simulations on materials and present some illustrative examples of applications to complex quasiperiodic alloys, cluster-support interactions in microporous acid catalysts and magnetic nanostructures.

We analyze the three-point vertex function that describes the coupling of fermionic particle-hole pairs in a metal to spin or charge fluctuations at nonzero momentum. We consider Ward identities, which connect two-particle vertex functions to the self-energy, in the framework of a Hubbard model. These are derived using conservation laws following from local symmetries. The generators considered are the spin density and particle density. It is shown that at certain antiferromagnetic critical points, where the quasiparticle effective mass is diverging, the vertex function describing the coupling of particle-hole pairs to the spin density Fourier component at the antiferromagnetic wave vector is also divergent. Then we give an explicit calculation of the irreducible vertex function for the case of three-dimensional antiferromagnetic fluctuations, and show that it is proportional to the diverging quasiparticle effective mass.

Classical densityfunctional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.

Densityfunctional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.

We study the bulk deformation properties of the Skyrme nuclear energy densityfunctionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear densityfunctional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy densityfunctionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.

Quantum state discrimination is a fundamental task in quantum information theory. The signals are usually nonorthogonal quantum states, which implies that they can not be perfectly distinguished. One possible discrimination strategy is the so-called Unambiguous State Discrimination (USD) where the states are successfully identified with non-unit probability, but without error. The optimal USD measurement has been extensively studied in the case of pure states, especially for any pair of pure states. Recently, the problem of unambiguously discriminating mixed quantum states has attracted much attention. In the case of a pair of generic mixed states, no complete solution is known. In this thesis, we first present reduction theorems for optimal unambiguous discrimination of two generic density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank r in a 2r-dimensional Hilbert space. These reduction theorems also allow us to reduce USD problems to simpler ones for which the solution might be known. As an application, we consider the unambiguous comparison of n linearly independent pure states with a simple symmetry. Moreover, lower bounds on the optimal failure probability have been derived. For two mixed states they are given in terms of the fidelity. Here we give tighter bounds as well as necessary and sufficient conditions for two mixed states to reach these bounds. We also construct the corresponding optimal measurement. With this result, we provide analytical solutions for unambiguously discriminating a class of generic mixed states. This goes beyond known results which are all reducible to some pure state case. We however show that examples exist where the bounds cannot be reached. Next, we derive properties on the rank and the spectrum of an optimal USD measurement. This finally leads to a second class of exact solutions. Indeed we present the optimal failure probability as well as the optimal measurement for

Nowadays, the search for efficient methods able to reduce the high atmospheric carbon dioxide concentration has turned into a very dynamic research area. Several environmental problems have been closely associated with the high atmospheric level of this greenhouse gas. Here, a novel system based on the use of surface-functionalized silicon quantum dots (sf-SiQDs) is theoretically proposed as a versatile device to bind carbon dioxide. Within this approach, carbon dioxide trapping is modulated by a photoinduced charge redistribution between the capping molecule and the silicon quantum dots (SiQDs). The chemical and electronic properties of the proposed SiQDs have been studied with a DensityFunctional Theory and DensityFunctional Tight-Binding (DFTB) approach along with a time-dependent model based on the DFTB framework. To the best of our knowledge, this is the first report that proposes and explores the potential application of a versatile and friendly device based on the use of sf-SiQDs for photochemically activated carbon dioxide fixation.

The combination of functional theory where the energy is written as a functional of the density, and the configuration mixing method, provides an efficient description of nuclear ground and excited state properties. The specific pathologies that have been recently observed, show the lack of a clear underlying justification associated to the breaking and the restoration of symmetries within densityfunctional theory. This thesis focuses on alternative treatments of pairing correlations in finite many body systems that consider the breaking and the restoration of the particle number conservation. The energy is written as a functional of a projected quasi-particle vacuum and can be linked to the one obtained within the configuration mixing framework. This approach has been applied to make the projection either before or after the application of the variational principle. It is more flexible than the usual configuration mixing method since it can handle more general effective interactions than the latter. The application to the Krypton isotopes shows the feasibility and the efficiency of the method to describe pairing near closed shell nuclei. Following a parallel path, a theory where the energy is written as a functional of the occupation number and natural orbitals is proposed. The new functional is benchmarked in an exactly solvable model, the pairing Hamiltonian. The efficiency and the applicability of the new theory have been tested for various pairing strengths, single particle energy spectra and numbers of particles. (author)

A useful kind of continuity of quantum states functions in asymptotic regime is so-called asymptotic continuity. In this letter, we provide general tools for checking if a function possesses this property. First we prove equivalence of asymptotic continuity with so-called robustness under admixture. This allows us to show that relative entropy distance from a convex set including a maximally mixed state is asymptotically continuous. Subsequently, we consider arrowing-a way of building a new function out of a given one. The procedure originates from constructions of intrinsic information and entanglement of formation. We show that arrowing preserves asymptotic continuity for a class of functions (so-called subextensive ones). The result is illustrated by means of several examples. (letter to the editor)

First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solve the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Lastly, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.

First-principles calculations combining density-functional theory and continuum solvation models enable realistic theoretical modeling and design of electrochemical systems. When a reaction proceeds in such systems, the number of electrons in the portion of the system treated quantum mechanically changes continuously, with a balancing charge appearing in the continuum electrolyte. A grand-canonical ensemble of electrons at a chemical potential set by the electrode potential is therefore the ideal description of such systems that directly mimics the experimental condition. We present two distinct algorithms: a self-consistent field method and a direct variational free energy minimization method using auxiliary Hamiltonians (GC-AuxH), to solve the Kohn-Sham equations of electronic density-functional theory directly in the grand canonical ensemble at fixed potential. Both methods substantially improve performance compared to a sequence of conventional fixed-number calculations targeting the desired potential, with the GC-AuxH method additionally exhibiting reliable and smooth exponential convergence of the grand free energy. Finally, we apply grand-canonical density-functional theory to the under-potential deposition of copper on platinum from chloride-containing electrolytes and show that chloride desorption, not partial copper monolayer formation, is responsible for the second voltammetric peak.

The risk that is created by nonlinear interactions among subjects in economic systems is assumed to increase during an abnormal state of a financial market. Nevertheless, investigating the systemic risk in financial markets following the global financial crisis is not sufficient. In this paper, we analyze the entropy densityfunction in the return time series for several financial markets, such as the S&P500, KOSPI, and DAX indices, from October 2002 to December 2011 and analyze the variability in the entropy value over time. We find that the entropy densityfunction of the S&P500 index during the subprime crisis exhibits a significant decrease compared to that in other periods, whereas the other markets, such as those in Germany and Korea, exhibit no significant decrease during the market crisis. These findings demonstrate that the S&P500 index generated a regular pattern in the return time series during the financial crisis.

Modeling of multiphase compositional hydrodynamics at nanoscale is performed by means of densityfunctional hydrodynamics (DFH). DFH is the method based on densityfunctional theory and continuum mechanics. This method has been developed by the authors over 20 years and used for modeling in various multiphase hydrodynamic applications. In this paper, DFH was further extended to encompass phenomena inherent in liquids at nanoscale. The new DFH extension is based on the introduction of external potentials for chemical components. These potentials are localized in the vicinity of solid surfaces and take account of the van der Waals forces. A set of numerical examples, including disjoining pressure, film precursors, anomalous rheology, liquid in contact with heterogeneous surface, capillary condensation, and forward and reverse osmosis, is presented to demonstrate modeling capabilities.

We introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in densityfunctional theory and Hartree endash Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix open-quote open-quote engine close-quote close-quote which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp parallel pp) class of integrals with speedups increasing to over ten times for (ff parallel ff) integrals. copyright 1996 American Institute of Physics

We investigate the role of the pion in covariant densityfunctional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the σ meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of densityfunctionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.

The local spin density approximation plus onsite Coulomb repulsion approach (LSDA+U) to densityfunctional theory is carefully reanalyzed. Its possible link to single-particle Green's function theory is occasionally discussed. A simple and elegant derivation of the important sum rules for the on-site interaction matrix elements linking them to the values of U and J is presented. All necessary expressions for an implementation of LSDA+U into a non-orthogonal basis solver for the Kohn-Sham equations are given, and implementation into the full-potential local-orbital solver (Phys. Rev. B 59 (1999) 1743) is made. Results of application to several planar cuprate structures are reported in detail and conclusions on the interpretation of the physics of the electronic structure of the cuprates are drawn

The validity of the Poisson and the λ P(k) modified Poisson statistical densityfunctions of observing k events in a short time interval is investigated experimentally in radioactive decay detection for various measuring times. The experiments to measure radioactive decay were performed with 89m Y, using a multichannel analyzer. According to the results, Poisson statistics adequately describes the counting experiment for short measuring times. (author) 13 refs.; 4 figs

The assumed joint probability densityfunction (PDF) between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid-scale (SGS) parameterization for boundary layer clouds and turbulent moments. This paper analyzes the performance of five families of PDFs using large-eddy simulations of deep convection, shallow convection, and a transition from stratocumulus to trade wind cumulus. Three of the PD...

The possible structure of Cu 6 cluster has been given with the GaussView that is a graphical user interface software. The structure optimization was performed on the B3LYP functional and SDD basic set of the quantum computational software of Gaussian03. And eight isomers of Cu 6 cluster were calculated. The binding energy and the structure of eight isomers have been investigated in detail. The result showed that the value of the binding energy was in reasonable agreement with available experimental data, as well as with other theoretical results, and the most stable structure was the triangle of plane. Three new isomers of the Cu 6 cluster have been got in our work, which would be the valuable data for the further theoretical and experimental study. (authors)

The intraband transitions which are essential for quantum dot intermediate band solar cells (QD IBSCs) are theoretically investigated by estimating the matrix elements from a ground bound state, which is often regarded as an intermediate band (IB), to conduction band (CB) states for a structure with a quantum dot (QD) embedded in a matrix (a QD/matrix structure). We have found that the QD pushes away the electron envelope functions (probability densities) from the QD region in almost all quantum states above the matrix CB minimum. As a result, the matrix elements of the intraband transitions in the QD/matrix structure are largely reduced, compared to those calculated assuming the envelope functions of free electrons (i.e., plane-wave envelope functions) in a matrix structure as the final states of the intraband transitions. The result indicates the strong influence of the QD itself on the intraband transitions from the IB to the CB states in QD IBSC devices. This work will help in better understanding the problem of the intraband transitions and give new insight, that is, engineering of quantum states is indispensable for the realization of QD IBSCs with high solar energy conversion efficiencies. (paper)

The Plato package allows both orthogonal and non-orthogonal tight-binding as well as densityfunctional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation. Program summaryProgram title: Plato Catalogue identifier: AEFC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 219 974 No. of bytes in distributed program, including test data, etc.: 1 821 493 Distribution format: tar.gz Programming language: C/MPI and PERL Computer: Apple Macintosh, PC, Unix machines Operating system: Unix, Linux and Mac OS X Has the code been vectorised or parallelised?: Yes, up to 256 processors tested RAM: Up to 2 Gbytes per processor Classification: 7.3 External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTW Nature of problem: Densityfunctional theory study of electronic structure and total energies of molecules, crystals and surfaces. Solution method: Localised orbital based densityfunctional theory. Restrictions: Tight-binding and densityfunctional theory only, no exact exchange. Unusual features: Both atom centred and uniform meshes available

. To demonstrate the capabilities of PE-MC-srDFT, we also investigated the retinylidene Schiff base chromophore embedded in the channelrhodopsin protein. While using a much more compact reference wave function in terms of active space, our PE-MC-srDFT approach yields excitation energies comparable in quality......We present here the coupling of a polarizable embedding (PE) model to the recently developed multiconfiguration short-range densityfunctional theory method (MC-srDFT), which can treat multiconfigurational systems with a simultaneous account for dynamical and static correlation effects. PE......-MC-srDFT is designed to combine efficient treatment of complicated electronic structures with inclusion of effects from the surrounding environment. The environmental effects encompass classical electrostatic interactions as well as polarization of both the quantum region and the environment. Using response theory...

We analyze the methodology and the performance of subsystem densityfunctional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method.

Ground-state energies for antiferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the densityfunctional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains.

We apply standard densityfunctional theory at the generalized gradient approximation (GGA) level to study the stability of rutile metal oxides. It is well known that standard GGA exchange and correlation in some cases is not sufficient to address reduction and oxidation reactions. Especially...... and due to a more accurate description of exchange for this particular GGA functional compared to PBE. Furthermore, we would expect the self-interaction problem to be largest for the most localized d orbitals; that means the late 3d metals and since Co, Fe, Ni, and Cu do not form rutile oxides...

We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.

We explore the local and nonlocal response functions of the grand canonical potential densityfunctional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the densityfunctional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model

In this paper a method is first presented to construct an Energy DensityFunctional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach. (orig.)

We introduce an ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Zémor and generalized bicycle codes by MacKay as limiting cases. The construction allows for both the lower and the upper bounds on the minimum distance; they scale as a square root of the block length. Many thus defined codes have a finite rate and limited-weight stabilizer generators, an analog of classical low-density parity-check (LDPC) codes. Compared to the hypergraph-product codes, hyperbicycle codes generally have a wider range of parameters; in particular, they can have a higher rate while preserving the estimated error threshold.

We give an introduction to certain topics from functional analysis which are relevant for physics in general and in particular for quantum mechanics. Starting from some examples, we discuss the theory of Hilbert spaces, spectral theory of unbounded operators, distributions and their applications and present some facts from operator algebras. We do not give proofs, but present examples and analogies from physics which should be useful to get a feeling for the topics considered. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

We give an introduction to certain topics from functional analysis which are relevant for physics in general and in particular for quantum mechanics. Starting from some examples, we discuss the theory of Hilbert spaces, spectral theory of unbounded operators, distributions and their applications and present some facts from operator algebras. We do not give proofs, but present examples and analogies from physics which should be useful to get a feeling for the topics considered. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

We derive corrections to the Schroedinger equation which arise from the quantization of the gravitational field. This is achieved through an expansion of the full functional Wheeler-DeWitt equation with respect to powers of the Planck mass. We demonstrate that the corrections terms are independent of the factor ordering which is chosen for the gravitational kinetic term. Although the corrections are numerically extremely tiny, we show how they lead, at least in principle, to shift in the spectral lines of hydrogen type atoms. We discuss the significance of these corrections for quantum field theory near the Planck scale. (author). 35 refs

Molecular dynamics with densityfunctional theory has emerged over the last two decades as a powerful and accurate framework for calculating thermodynamic and transport properties with broad application to dynamic compression, high energy density science, and warm dense matter. These calculations have been extensively validated against shock and ramp wave experiments, are a principal component of high-fidelity equation of state generation, and are having wide-ranging impacts on inertial confinement fusion, planetary science, and shock physics research. In addition to thermodynamic properties, phase boundaries, and the equation of state, one also has access to electrical conductivity, thermal conductivity, and lower energy optical properties. Importantly, all these properties are obtained within the same theoretical framework and are manifestly consistent. In this talk I will give a brief history and overview of molecular dynamics with densityfunctional theory and its use in calculating a wide variety of thermodynamic and transport properties for materials ranging from ambient to extreme conditions and with comparisons to experimental data. I will also discuss some of the limitations and difficulties, as well as active research areas. Sandia is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Full Text Available Quantum chemical calculations at the B3LYP/6–31G* level of theory were employed for the structure-activity relationship and prediction of the antioxidant activity of edaravone and structurally related derivatives using energy (E, ionization potential (IP, bond dissociation energy (BDE, and stabilization energies (∆Eiso. Spin density calculations were also performed for the proposed antioxidant activity mechanism. The electron abstraction is related to electron-donating groups (EDG at position 3, decreasing the IP when compared to substitution at position 4. The hydrogen abstraction is related to electron-withdrawing groups (EDG at position 4, decreasing the BDECH when compared to other substitutions, resulting in a better antioxidant activity. The unpaired electron formed by the hydrogen abstraction from the C–H group of the pyrazole ring is localized at 2, 4, and 6 positions. The highest scavenging activity prediction is related to the lowest contribution at the carbon atom. The likely mechanism is related to hydrogen transfer. It was found that antioxidant activity depends on the presence of EDG at the C2 and C4 positions and there is a correlation between IP and BDE. Our results identified three different classes of new derivatives more potent than edaravone.

Ab initio calculations of hydrogen-passivated Si nanowires were performed using densityfunctional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost.

Ab initio calculations of hydrogen-passivated Si nanowires were performed using densityfunctional theory within LDA-1/2, to account for the excited states properties. A range of diameters was calculated to draw conclusions about the ability of the method to correctly describe the main trends of bandgap, quantum confinement, and self-energy corrections versus the diameter of the nanowire. Bandgaps are predicted with excellent accuracy if compared with other theoretical results like GW, and with the experiment as well, but with a low computational cost

The spontaneous emission rate of excitons strongly confined in quantum dots (QDs) is proportional to the overlap integral of electron and hole envelope wave functions. A common and intuitive interpretation of this result is that the spontaneous emission rate is proportional to the probability...... that the electron and the hole are located at the same point or region in space, i.e., they must coincide spatially to recombine. Here, we show that this interpretation is not correct even loosely speaking. By general mathematical considerations we compare the envelope wave function overlap, the exchange overlap...... integral, and the probability of electrons and holes coinciding, and find that the frequency dependence of the envelope wave function overlap integral is very different from that expected from the common interpretation. We show that these theoretical considerations lead to predictions for measurements. We...

We compare quantum and classical machines designed for learning an N-bit Boolean function in order to address how a quantum system improves the machine learning behavior. The machines of the two types consist of the same number of operations and control parameters, but only the quantum machines utilize the quantum coherence naturally induced by unitary operators. We show that quantum superposition enables quantum learning that is faster than classical learning by expanding the approximate solution regions, i.e., the acceptable regions. This is also demonstrated by means of numerical simulations with a standard feedback model, namely random search, and a practical model, namely differential evolution. (paper)

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted ‘DBT’, provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic densityfunctional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision densityfunctional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-densityfunctionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the

Full Text Available Electron density is used to compute Shannon entropy. The deviation from the Hartree–Fock (HF of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy densityfunctional developed within Kohn–Sham theory. To this purpose, results from eight different functionals, representative of Jacob’s ladder, are compared with accurate results obtained from diffusion quantum Monte Carlo (DMC computations. For three series of atomic ions, our results show that the revTPSS and the PBE0 functionals are the best, whereas those based on local density approximation give the largest discrepancy from DMC Shannon entropy.

We have used two- and three-pulse femtosecond differential transmission spectroscopy to study the dependence of quantum dot carrier dynamics on temperature. At low temperatures and densities, the rates for relaxation between the quantum dot confined states and for capture from the barrier region into the various dot levels could be directly determined. For electron-hole pairs generated directly in the quantum dot excited state, relaxation is dominated by electron-hole scattering, and occurs on a 5 ps time scale. Capture times from the barrier into the quantum dot are of the order of 2 ps (into the excited state) and 10 ps (into the ground state). The phonon bottleneck was clearly observed in low-density capture experiments, and the conditions for its observation (namely, the suppression of electron-hole scattering for nongeminately captured electrons) were determined. As temperature increases beyond about 100 K, the dynamics become dominated by the re-emission of carriers from the lower dot levels, due to the large density of states in the wetting layer and barrier region. Measurements of the gain dynamics show fast (130 fs) gain recovery due to intradot carrier-carrier scattering, and picosecond-scale capture. Direct measurement of the transparency density versus temperature shows the dramatic effect of carrier re-emission for the quantum dots on thermally activated scattering. The carrier dynamics at elevated temperature are thus strongly dominated by the high density of the high energy continuum states relative to the dot confined levels. Deleterious hot carrier effects can be suppressed in quantum dot lasers by resonant tunnelling injection